8x + 5y = -3
-2x + y = 21
Solving by Substitution
First, we're going to find an equation for the value of a variable to plug it into the other equation in the system. -2x + y = 21 looks like it can easily be rearranged to get the equation for the value of y.
-2x + y = 21
Add 2x to both sides to isolate for the equation for the value of y. You should now have:
y = 2x + 21
Now that you have the equation for the value of y, you can plug the terms (2x + 21) into where y would appear in the other equation of the system. So:
8x + 5y = -3
8x + 5(2x + 21) = -3
Distribute. What this means is that you'll be multiplying 2x by 5 and 21 by 5. So:
5 * 2x = 10x
5 * 21 = 105
Re-write the equation:
8x + 10x + 105 = -3
Combine like terms (10x + 8 = 18x):
18x + 105 = -3
This is a two-step equation. Subtract 105 from both sides to cancel out 105 in order to get closer to finding the value of x.
18x = -108
Divide by 18 to isolate for x:
-108/18 = x
-108/18 = -6
x = -6
Plug the value of x back into the equation for the value of y to figure out y's value:
y = 2x + 21
y = 2(-6) + 21
y = -12 + 21
y = 9
Plug these values back into the whole system to prove they're right:
8x + 5y = -3
8(-6) + 5(9) = -3
-48 + 45 = -3
-3 = -3
-2x + y = 21
-2(-6) + 9 = 21
12 + 9 = 21
21 = 21
These are the correct values.