How do you solve the system of equations by graphing 8x + 5y = -3 and -2x + y = 21 and then classify the system?

1 Answer
Jun 4, 2018

x = -6
y = 9

Explanation:

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.