what is linear combination and how do you do this problem?

Question

x+y=4
2x-y=2

Answer 1

First, you multiply the top equation by 2, to get:

2x+2y = 8
2x - y = 2

Then, subtract the top equation with the bottom equation. That is,
(2x+2y) - (2x - y) = 8 - 2
2x + 2y - 2x + y = 6
3y = 6
y = 2

Now that you know the value of y, you can now solve for x, using any one of those two equations. Let's use the second one.

2x - y = 2
2x - (2) = 2
2x - 2 = 2
2x = 4
x = 2

Therefore, x=2 and y=2 is the solution.

Answer 2

this is a system of equation
if you graphed these two lines and they intersect, then the intersection would be some x,y point and that would be your answer

x + y = 4
2x - y = 2

add the two equations together to get rid of y

3x = 6
x = 2

plug x back into one of the equations to find y
x + y = 4
2 + y = 4
y = 2

thus the answers are
x = 2
y = 2

Answer 3

x+y=4
2x-y=2 you add these linear equations & get
3x=6 divide by 3
x=2

substitute
2+y=4 subtract 2
y=2

solution is (2,2)