Question

use substitution to solve: 3x - 2y = 9 and 2x + 5y = 19

Answer 1

Solve one of the equations for x and then substitute this equation into the other one.

Answer 2

So solving 3x - 2y = 9 for x we get:
x=(9+2y)/3

Answer 3

then we substitute x=(9+2y)/3 into 2x + 5y = 19 in order to solve for y:

2[(9+2y)/3] + 5y = 19
[(18+4y)/3]+5y=19
18+4y=(19-5y)*3
18+4y=57-15y
15y+4y=57-18
19y=39
y=39/19

Answer 4

Now we can substitute y=39/19 into x=(9+2y)/3 to get the value of x:

x=(9+2y)/3
x=[9+2(39/19)]/3
x=83/19