Answer:
(4,-2)
Step-by-step explanation:
What is linear combination?
Linear combination is the process of adding two equations to eliminate a variable so that we are able to solve for the other variable.
Here we are given the two equations 9x + 4y = 28 and 2x + 4y = 0. We can use linear combination to cancel out the two 4y terms leaving us with only x variables in which we can solve for.
Adding the two equations. (subtracting the second equation from the first) we really are subtracting the second equation from the first because if we were to add we would get 4y + 4y which wouldn't cancel out the terms therefore we would have to subtract the two equations to get 4y - 4y which cancels out the terms.
9x + 4y = 28
- (2x + 4y = 0)
==> remove parenthesis and apply negative sign
9x + 4y = 28
-2x - 4y = -0
----------------------
7x = 28
==> divide both sides by 7
x = 4
Finding the y value:
The solution is written as (x,y) meaning we also need the value of y. To find it we can plug in the value of x into one of the equations and then we can solve for y.
2x + 4y = 0
==> plug in x = 4
2(4) + 4y =0
==> multiply 2 and 4
8 + 4y = 0
==> subtract 8 from both sides
4y = -8
==> divide both sides by 4
y = -2
so we have x = 4 and y = -2
the solution of the equation would be (4,-2)
Checking our work
If our answer is correct we can plug in the values of x and y into both equations and the outcome will be valid ( or correct )
Equation 1 : 9x + 4y = 28
==> plug in x = 4 and y = -2
9(4) + 4(-2) = 28
==> multiply 9 and 4
36 + 4(-2) = 28
==> multiply 4 and -2
36 - 8 = 28
==> subtract 8 from 36
28 = 28
Equation 2 : 2x + 4y = 0
==> plug in x = 4 and y = -2
2(4) + 4(-2) = 0
==> multiply 2 and 4
8 + 4(-2) = 0
==> multiply 4 and -2
8 - 8 = 0
==. Subtract 8 from 8
0 = 0
Both are correct so our solution is correct!
Learn more about solving systems using linear combination here! : https://brainly.com/question/12691830
