Question

If you were to solve the following system by substitution, what would be the best variable to solve for and from what equation?

3x+6y=9

2x-10y=13

A) x, in the second equation
B) y, in the first equation
C) y, in the second equation
D) x, in the first equation

Answer 1

3x+6y=9 would be the best choice, since all of its terms are divisible by 3:

x+2y = 3, so x=3-2y

Subbing this result into 2x-10y=13 turns out 2(3-2y) - 10y = 13, or

6 - 4y - 10y = 13

6 - 14y = 13

-14y = 7, and thus y = -1/2. Then x = 3-2y (as found earlier), and
x = 3-2(-1/2) = 3+1 = 4

The solution is (4, -1/2).