Question

Solve the system of linear equations by substitution.−2x−5y=3 3x+8y=−6

Answer 1

First you want to know what y or x is i chose y for this on 

so the equation i'm going to use is -2x-5y=3
i want to solve for y

-2x-5y=3
+2x        +2x

-5y=2x+3
 /-5   /-5  /-5
y=-2/5x+-3/5

Now that i solved for y we substitute our answer into the next equation to solve for x like this:

3x+8y=-6
3x+8(-2/5x+-3/5)=-6
3x+ -3.2x+-4.8=-6
-0.2x+-4.8=-6
          +4.8  +4.8
-0.2x=-1.2
/-0.2    /-0.2
x=6

After you know what x is you substitute it in for any of the equations that we started with. I picked 3x+8y=-6 to find y.

3x+8y=-6
3*6+8y=-6
18+8y=-6
-18      -18
8y=-24
/8     /8
y=-3

Since we know what x and y are we substitute it with any of the equations that we started with. i picked -2x-5y=3

-2*6-5*-3=3
-12- -15=3
3=3 
so our solution (6,-3) works