8x + 5y = -38x+5y=−3
-2x + y = 21−2x+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 = 21−2x+y=21 looks like it can easily be rearranged to get the equation for the value of yy.
-2x + y = 21−2x+y=21
Add 2x2x to both sides to isolate for the equation for the value of yy. You should now have:
y = 2x + 21y=2x+21
Now that you have the equation for the value of yy, you can plug the terms (2x + 21)(2x+21) into where yy would appear in the other equation of the system. So:
8x + 5y = -38x+5y=−3
8x + 5(2x + 21) = -38x+5(2x+21)=−3
Distribute. What this means is that you'll be multiplying 2x2x by 55 and 2121 by 55. So:
5 * 2x = 10x5⋅2x=10x
5 * 21 = 1055⋅21=105
Re-write the equation:
8x + 10x + 105 = -38x+10x+105=−3
Combine like terms (10x + 8 = 18x)(10x+8=18x):
18x + 105 = -318x+105=−3
This is a two-step equation. Subtract 105105 from both sides to cancel out 105105 in order to get closer to finding the value of xx.
18x = -10818x=−108
Divide by 1818 to isolate for xx:
-108/18 = x−10818=x
-108/18 = -6−10818=−6
x = -6x=−6
Plug the value of xx back into the equation for the value of yy to figure out yy's value:
y = 2x + 21y=2x+21
y = 2(-6) + 21y=2(−6)+21
y = -12 + 21y=−12+21
y = 9y=9
Plug these values back into the whole system to prove they're right:
8x + 5y = -38x+5y=−3
8(-6) + 5(9) = -38(−6)+5(9)=−3
-48 + 45 = -3−48+45=−3
-3 = -3−3=−3
-2x + y = 21−2x+y=21
-2(-6) + 9 = 21−2(−6)+9=21
12 + 9 = 2112+9=21
21 = 2121=21
These are the correct values.
