SAT: Systems of Equations

Question

3x + 4y = -23

2y - x = -19

What is the solution (x,y) to the system of equations above?

Answer 1

Systems can be solved three ways: graph (see where the graphs intersect), substitution or elimination.

(1) 3x + 4y = -23

(2) 2y - x = -19

Here, substitution is best because equation (2) can be re-written to x = 2y + 19 and substituted into equation (1)

3(2y + 19) + 4y = -23

6y + 57 + 4y = -23

10y = -80

y = -8

2(-8) - x = -19

-16 - x = -19 or x = -16 + 19; x = 3

Check by substituting back into both original equations.

Answer 2