Question

Solve by the linear combination method (with or without multiplication).
2x + 8y = –2
5x + 6y = 9

A. (3, –1)
B. (–2, 2)
C. (–2, 7)
D. (–1, 3)

Answer 1

Do you know substitution (or combination method I guess is what your textbook is calling it)?
It's when you isolate a variable in one of the equations.

For example, #1: 2x + 8y = -2
If you subtract (8y) from both sides, you end up with: 2x = -8y - 2
Now you divide 2 on both sides to isolate the variable "x" so : x = (-8/2)x - (2/2) or x = -4y - 1

So think... if x = -4y -1, and in the second equation, which is related to the first, 5x + 6y = 9
then can't we simply put what "x" is, which we know is "-4y - 1", into the second equation.
We end up with: 5 (-4y - 1) + 6y = 9

Now distribute the 5 first to the "-4y" and the "-1" and you get:
-20y - 5 + 6y = 9
Combine like terms:
-14y - 5 = 9
Add (5) to both sides:
-14y = 14
Divide both sides by (-14) and you get:
y = -1

Now all you do is plug in (-1) for "y" in one of the equations (doesn't matter which) and find x.
So lets use the first equation:
2x + 8y = -2
Plug in (-1) for y:
2x + 8(-1) = -2
Multiply:
2x + (-8) = -2
Add (8) to both sides:
2x = 6
Finally divide by 2:
x = 3

The format for a set of equations is (x,y) so the answer is (3,-1) which is (A)

Keep in mind that you could have solved for any variable in the beginning. I just chose "x" because it seemed simpler. Please use this as an example for the rest of your problems. If you need extra explanations, just reply.