Use the linear combination method to solve the system of equations. Please explain each step of your solution
2x - 3y = 13
x + 2y = -4
Answers
Answer:
(2, -3)
Solve the equation
\(\left \{ {{2x-3y=13} \atop {x+2y=-4}} \right.\)
Rearrange like terms to the same side of the equation
\(\left \{ {{2x-3y=13} \atop {x=-4-2y}} \right.\)
Substitute into one of the equations
\(2(-4-2y)-3y=13\)
Apply the Distributive Property
\(-8-4y-3y=13\)
Combine like terms
\(-8-7y=13\)
Rearrange variables to the left side of the equation
\(-7y=13+8\)
Calculate the sum or difference
\(-7y=21\)
Divide both sides of the equation by the coefficient of variable
\(y=-\frac{21}{7}\)
Cross out the common factor
\(y=-3\)
Substitute into one of the equations
\(x=-4-2\times(-3)\)
Calculate
\(x=2\)
The solution of the system is
\(\left \{ {{x=2} \atop {y=-3}} \right.\)
I hope this helps you
:)
Related Questions
please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!
Answers
The function for the points are y = -15x - 5
How to determine the functionFrom the information given, we have that;
The points are;
(1/3,0) (-2 3/4,0) and (0,-5)
Using the point-slope form of a linear equation, we have;
y - y₁ = m(x - x₁)
Such that;
m is the slope of the liney - y₁ and (x - x₁) are the pointsUsing (1/3, 0) and (0, -5), we have that the slope is;
m = (0 - (-5))/0 -1/3)
expand the bracket
= 5 / (-1/3)
= -15
Now, take any of the given points and substitute the values
Using (1/3, 0), we get;
y - 0 = -15(x - 1/3).
y = -15x - 5.
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The function for the points solved by (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)
We have given the points:
(1/3,0) (-2 3/4,0) and (0,-5)
Using the formula of linear equation
\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)
Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)
that is 1/3 = \(a\), 0 = \(a_{1}\) and
0 = \(b\), -5 = \(b_{1}\)
\(x\) refers to the slope of line (take any variable)
Now for finding the value of \(x\),
\(x=a-a_{1}/b-b_{1}\)
inserting the values,
\(x=[0-[-5]]/[0-1/3]\\x= -15\)
Substitute the value of \(x\) in the equation
\(a-0=-15[b-1/3]\)
By simplifying the equation, we get
\(a=-15b-5\)
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Please help me I need help with this what is the answer to:
-8 + m = -20
Answers
-8 + m = -20
Add similar terms
-20 + 8 = -12
M = -12 should be correct.
Answer:
m=−12
−8+m=−20
Add 8 to both sides.
m=−20+8
Add −20 and 8 to get −12.
therefore are answer is m= -12
Please help me .....
Answers
Answer:
Step-by-step explanation:
Starting from the top and going clockwise
(3,8)
(0,6)
(0,2)
(1,1)
(3,5)
Ex (-4,2) is (0, 2) and (-7,4) is (3,4)
so basically the y stays the same and the x changes based on how far is is from the line of reflection. there is also probably a better way to do this but it’s 2 am so yea
A group of seventh graders and a group of teachers at a local middle school were asked how many siblings they each have. The dot plots below show the results. Students A dot plot titled Students. A number line going from 0 to 9 labeled number of siblings. There are 2 dots above 0, 4 above 1, 7 above 2, 5 above 3, 2 above 4, and 0 above 5, 6, 7, 8, and 9. Teachers A dot plot titled Teachers. A number line going from 0 to 9 labeled Number of siblings. There is 1 dot above 0, 3 dots above 1, 2 above 2, 4 above 3, 5 above 4, 3 above 5, 1 above 6, 0 above 7, 1 above 8, and 0 above 9. When comparing the shape of the two sets of data, what conclusion can someone draw? The students tend to have fewer siblings than the teachers. The teachers tend to have fewer siblings than the students. Both the students and the teachers have a wide range of siblings. Both sets of data have the same shape. the answer is- a. The students tend to have fewer siblings than the teachers.
Answers
Answer:
A. The students tend to have fewer siblings than the teachers.
Step-by-step explanation:
First we need to draw the dot plots correctly. If you count both sides they have 20 each.
Now, clearly none have fewer nobody here yet has more or less but going on to the next step.
Multiply exactly the number of siblings times how many people chose that many siblings. Ex: 2 (siblings) times 7 (people who has 2 siblings) = 14. And so on.
On the Student A, we get a total of 41 people having sibling, if you count the 0's then there were a total of 43 people. But now on the Teacher's A Dot Plot, we have a total of 68 people, if you include the 0 then we have a total of 69.
So the answer is A. The students tend to have fewer siblings than the teachers.
Answer:
The sum is A
Step-by-step explanation:
Just ma duty to help the community
the ratio of the number of oranges to apples to bananas is 8:5:2. if there are 120 fruits in total, how many bananas are there
Answers
Answer:
Step-by-step explanation:
To find the number of bananas, we need to determine the proportion of bananas in the total number of fruits based on the given ratio.
Let's assume that the ratio of oranges, apples, and bananas can be represented by 8x, 5x, and 2x, respectively, where x is a common multiplier.
The sum of the parts in the ratio is 8x + 5x + 2x = 15x.
We know that the total number of fruits is 120. Therefore, we can set up the following equation:
15x = 120
To solve for x, we divide both sides of the equation by 15:
x = 120 / 15
x = 8
Now that we know the value of x, we can find the number of bananas by multiplying it by the corresponding part of the ratio:
Number of bananas = 2x = 2 * 8 = 16
So, there are 16 bananas in total.
We can add all the parts to the ratio and get 15. Out of 15 parts, 2 are bananas. Now we can calculate how many fruits are in one part. One fifteenth of 120 is 8, so there are 8 fruits in one part. 2 parts are bananas, so multiplying 8 with 2 gives us our answer, 16.
Order the numbers from closest to zero to farthest from zero:
4.38, l4.5l, l-4.6l, -l4.9l
HELPPPPP
Answers
The smallest number is the one closest to zero, or after zero, if it's a negative number, while the largest number is the number with the largest difference from the smallest, or the highest of value (not considering all situations). Usually, you would use the ascending order method for graphing numbers based on their value, which is indeed smallest to largest. According to thefreedictionary.com, "A function or variable continuously approaching zero as a limit." Tip: In ordering numbers based on value, the whole numbers that aren't negative are considerably believed to be the easiest numbers to order.
With that being said, here is the order of the numbers from smallest to largest:
4.38
4.5
4.6
4.9
Answer:
Here are the numbers ordered from closest to zero to farthest from zero:
4.38 (closest to zero)
4.5
-4.6
-4.9 (farthest from zero)
Step-by-step explanation:
Jason enjoys walking around the block with his dog, Ringo. When Jason and Ringo walk w times around the block, they walk 0.75w miles. Last week, Jason and Ringo walked 12 times around the block.
How many miles did Jason and Ringo walk around the block last week?
Write your answer as a whole number or decimal.
Answers
Show your work and write an expression using the following criteria:
A dividend is greater than 1,000
The quotient is 52 with a remainder of 18
please help me, fast!
Answers
Dividend (D) > 1,000
Quotient = 52
Remainder = 18
Based on these criteria, we can set up the equation as follows:
D = Quotient × Divisor + Remainder
Since the quotient is 52 and the remainder is 18, the equation becomes:
D = 52 × Divisor + 18
To meet the criteria that the dividend is greater than 1,000, we need to find a suitable value for the divisor. We can do that by rearranging the equation:
D - 18 = 52 × Divisor
Now, let's choose a value for D that is greater than 1,000. For example, let's use D = 1,500:
1,500 - 18 = 52 × Divisor
1,482 = 52 × Divisor
Dividing both sides by 52:
Divisor = 1,482 / 52
Simplifying:
Divisor ≈ 28.5
Therefore, the expression that satisfies the given criteria is:
Dividend (D) = 1,500
Quotient = 52
Remainder = 18
Divisor ≈ 28.5
The equation becomes:
1,500 = 52 × 28.5 + 18
the graph shows a proportional relationship between the cups of flour a baker uses and the number of cookies made
A. what does the point 0 0 represent in the situation
B. what does the point (1,18) represent
Answers
Answer:
point of origin is 0,0 coordinate is 1,18
Step-by-step explanation:
Quadratic functions r and s are graphed on the same coordinate grid. The vertex of graph r is 2 units to the left of the vertex of the graph of s. Which pair of functions could be used to create the graphs of r and s?
a.r(x)=(x+2)^2
s(x)=x^2
b.r(x)=x^2-2
s(x)=x^2
c.(x)=x^2+2
s(x)=x^2
d.(x)=(x-2)^2
s(x)=x^2
Answers
Answer:
not shoreeeeeeeeeeee
Step-by-step explanation:
i do apologize
Water makes up about 71% of the Earth’s surface, while the other 29% consists of continents and islands. 96% of all the Earth’s water is contained within the oceans as salt water, while the remaining 4% is fresh water located in lakes, rivers, glaciers, and the polar ice caps.
The total volume of water on Earth is 1,386 million cubic kilometers.
a. What is the volume of salt water.
b. What is the volume of fresh water.
Answers
Answer:
a. what is the volume of salt water.
explanation:
So 71 percent of the earth's surface is water and that water is broken down as salt, water and fresh water, so 96 percent of 71 percent is salt.
Answer:
Step-by-step explanation:
Figure out how much salt is in 1 liter of the ocean water. Then multiply it the number of liters there are
Here are the results from the softball throw event on field day. The event took place on the football field. The distance the ball was thrown was measured as a portion of the field.
Nina: 1/4
Paul: 0.17
Richard: 22%
Tito: 0.28
Bart: 3/7
Julie: 2/9
1. Who threw the softball the farthest on the football field?
2. List the people who threw the ball from shortest distance to largest distance.
Answers
Tito 28%
Nina 25%
Julie 22.2%
Richard 22%
Paul 17%
Select the equation that correctly describes the following real-world situation.
15 pieces of candy are given to s students from a bag of candy containing 310 pieces. There are 10 pieces left over.
A (s x 15) ÷ 10 = 310
B (s + 15) = 310 ÷ 10
C (310 − 10) ÷ 15 = s
D 310 ÷ (s + 15) = 10
Answers
Answer: C
Step-by-step explanation:
The equation that is correct is this one ⇒ (310 − 10) ÷ 15 = s
We know that there are 10 pieces left over, so we can subtract that from our total amount. (310-10)
Then, we know that the rest of the candy was given to s students, hence (310 − 10) ÷ 15 = s.
BONUS -To solve the equation:
(310 − 10) ÷ 15 = s
300 ÷ 15 = s
s=20
Good luck on your homework!
Tobin is solving the equation 3 (x minus 1.25) = 11.25. His work is shown below.
3 (x minus 1.25) = 11.25. 3 x minus 3.75 = 11.25. 3 x minus 3.75 + 3.75 = 11.25 + 3.75. 3 x = 15. 3 x times 3 = 45 times 3. x = 135.
Answers
Answer:
Step-by-step explanation:
5. Here is a shape with some measurements in cm.
Answers
Answer:
Just saying that there are links people post that scam you and this is requird by Brainly
Step-by-step explanation:
The table is completed below.
We can say that the relationship between the scale factor and the area of scaled copies is proportional.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
Using the formula for the area of a triangle:
Area = 1/2 x base x height
With a base of 3cm and height of 2cm, the area of the original triangle is:
Area = 1/2 x 3cm x 2cm = 3cm²
To find the area of the scaled triangles, we can use the scale factor to determine the corresponding dimensions, and then calculate the area using the same formula.
Scale factor Corresponding dimensions Area
1 3cm x 2cm 3cm²
2 6cm x 4cm 12cm²
5 15cm x 10cm 75cm²
s 3s cm x 2s cm 3s² cm²
Now,
To see if the relationship between the scale factor and the area of scaled copies is proportional, we can calculate the ratio of the area to the scale factor for each row of the table:
Scale factor Corresponding dimensions Area Ratio of area to scale factor
1 3cm x 2cm 3cm² 3/1 = 3
2 6cm x 4cm 12cm² 12/2 = 6
5 15cm x 10cm 75cm² 75/5 = 15
s 3s cm x 2s cm 3s² cm² (3s²)/s = 3s
In each case, the ratio of the area to the scale factor is constant, which means that the relationship between the scale factor and the area of scaled copies is indeed proportional.
Therefore,
We can say that the relationship between the scale factor and the area of scaled copies is proportional.
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need answer for these qyestion
Answers
thank you for asking me this question
Answer for question 4 is 30
10x20 to the power of 5
Answers
Answer:
24,300,000
Step-by-step explanation:
Please help quick! this is my second to last question!
Answers
Answer:
1.) 17
2.) -6
3.) 6
4.) 14
5.) -13
Step-by-step explanation:
1. 2x8+1= 17
2. 10 - (4x4)= 10-16= -6
3. (10/5) + 4 = 2+4= 6
4. (-6 x 1/3) + 16= -2 + 16= 14
5. (8 x -1) - 5= -8 - 5= -13
1.) 17
2.) -6
3.) 6
4.) 14
5.) -13
What is the distance between the points (-8, -3) and (-2,-5)?
Answers
Answer:
Step-by-step explanation:
\(Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\=\sqrt{(-2-[-8])^{2}+(-5-[-3])^{2}}\\\\=\sqrt{(-2+8)^{2}+(-5+3)^{2}}\\\\=\sqrt{(6)^{2}+(-2)^{2}}\\\\=\sqrt{36+4}\\\\ =\sqrt{40}\\\\=\sqrt{2*2*2*5}\\\\=2\sqrt{2*5}\\\\=2\sqrt{10}\\\)
The answer is 2√10 units.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
For the equation, determine whether the equation is true for all, some, or no values of x.
Explain how you know.
Answers
Answer:
You can check if an equation is true for all some or no values of x by simply to try and solve the equation if you get something like x = x, then the equation is true for all, if you get a specific answer like x=3, then it is true to some values, in simple terms. Try and solve the equation there is no other way to check unless you solve, I don't know if there is another way but this is just my intution.
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
111
A deli offers a lunch-special that comes with soup, a sandwich, and a dessert. The soup choices are tomato or onion, the sandwich choices are ham, chicken, tuna, or pastrami, and the dessert choices are cake or pie.
a. Would this problem best be solved by using a table, a list, or a tree diagram. Explain your answer.
b. Use one of those methods to determine the size of the lunch-special sample space.
Answers
Answer:
A. This problem would best be solved using a tree diagram.
B. In order to solve it, you would construct a tree with the first soup choices growing into the other options. Then, after listing every alternative, you could either add them all up to obtain your answer or you could just use the formula 2*4*2=16, which would result in 16 possibilities.
please please pleaseeee help I beg you ill give 25 points please
Answers
Answer:nonlinear i think
Step-by-step explanation:
Which scenario can be modeled by the linear function
y = -15x + 500?
A. The temperature on Jupiter is
15℉ and increases by 500℉ every day.
B. There is a population of 500 giraffes in Western Africa that decreases by 15 giraffes each year.
C. A carpet cleaning service charges $500 plus an additional $15 for every hour.
D. A membership fee for a movie streaming service is free, but each rental costs $15.
Answers
If point D' is the image of D(-2,1) under a reflection across the x-axis. What are the coordinates of D'?
Answers
Answer:
(-2, -1)
Step-by-step explanation:
When reflecting across the x-axis, the x coordinate remains the same, but the y-coordinate turns to its opposite. So to get D from D', keep -2, and make 1 a -1.
Please Hurry. I need this answer quickly please.
Answers
Answer:63
Step-by-step explanation:
multiply 72 by 7 then divide i by 8
(72×7)/8
=63
It's 63.
simplify the equation 7/8×72 multiple 7×9 solution is 63
HELP ME PLEASE REALLY IMPORTANT OR ILL GET IN TROUBLE!! WILL MARK AS BRAINLEST IF YOU GET IT CORRECT!!
Answers
Answer:
7
Step-by-step explanation:
The area of Angelo's circular kitchen table is 28.26 square feet. When two people sit across from each other at the table, how far apart are they?
(Pls help step-to-step)
Answers
Answer:177.472
Step-by-step explanation:
\(2\pi r\)
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
Answers
2 2/3 divided by 5 2/3 = 8/3 divided by 17/3 = 8/17 hours per mile
Answer:
5 2/3 divided by 2 2/3 = 17/3 divided by 8/3 = 17/8 = 2 1/8 miles per hour
2 2/3 divided by 5 2/3 = 8/3 divided by 17/3 = 8/17 hours per mile
Step-by-step explanation:
Given the equation, y= ; x-4, what is the slope and the y-intercept?
Om= 4 and be
-Im-1
1
Om=-4 and b=
3
Om=
and b=4
3
Om=
11/ 을
and b = -4
w
NEXT QUESTION
ASK FOR HELP
Answers
Answer: Slope is 1 because if we have x by itself, we assume it is only one.
y-intercept because according to the slope intercept formula, (y=mx+b), it is in the correct spot.
What is payroll tax ???????????????????????????????????????????????????????????????
Answers
Answer:
The individual income tax (or personal income tax) is a tax levied on the wages, salaries, dividends, interest, and other income a person earns throughout the year. The tax is generally imposed by the state in which the income is earned.
Step-by-step explanation:
Payroll tax refers to the taxes that are deducted from an employee's wages or salary by their employer.
We have to give that,
To define Payroll tax.
Now, Payroll tax refers to the taxes that are deducted from an employee's wages or salary by their employer.
These taxes are withheld to fund various government programs and services.
Payroll taxes typically include federal, state, and local income taxes, as well as Social Security and Medicare taxes.
The amount of payroll taxes deducted from an employee's paycheck depends on factors such as income level, tax brackets, and the tax rates set by the applicable government authorities.
These taxes are then remitted by the employer to the appropriate tax agencies on behalf of their employees.
They are specifically related to employment income and play a crucial role in funding important government initiatives and social programs.
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