Question

Answers to these systems of two equations

4x+2y=10
x-y=13

Answer 1

4x+2y=10

Plug in y+13 where x is on the other system.

So 4x+2y=10 would be 4(y+13)+2y=10

4(y+13)+2y=10
4y+ 52+2y=10
6y=-42 (Result of adding 4y and 2y, and subtracting 52 on both sides)
y=-7 (Result of dividing both sides by 6, finding what y equals!)

That's the first step. Right now our answer looks like this: (x, -7). We need to find what x is equal to. If we know what y is equal to we can just plug that in wherever y is. From here you can choose either of the equations. We'll go with the easier one, 4x+2y=10.

4x+2y=10
4x+2(-7)=10 (As a result of plugging in -7 for y)
4x+(-14)=10 (The equation above simplified)
4x=24 (Result of adding 14 to each side)
x=6 (Result of dividing each side by 4, finding our final answer!)

Now that we know what x and y are equal to, you now have the answer.

The answer to the system is (6, -7)

Answer 2

`4x+2y=10 \\ x-y=13 \ \ \ |* 2 \\ \\ 4x+2y=10 \\ \underline{2x-2y=26} \\ 4x+2x=10+26 \\ 6x=36 \ \ \ |/ 6 \\ x=6 \\ \\ x-y=13 \\ 6-y=13 \ \ \ |-6 \\ -y=7 \ \ \ |* (-1) \\ y=-7 \\ \\ \boxed{(x,y)=(6,-7)}`