Solve using substitution. –4x + 2y = –16, 8x − 2y = 12

Question

solving this on ixl

Answer 1

Hello, thank you for taking the time to post your question!

This is your system of equations:

-4x + 2y = -16

8x – 2y = 12

So you want to start by solving for one of the variables … I would do “y” in the first equation

-4x + 2y = -16

2y = 4x – 16

y = 2x – 8

then plug that back into the second equation to get it down to a single variable

8x – 2(2x – 8) = 12

8x – 4x + 16 = 12

4x = -4

x = -1

plugging that back into the equation for y gives

y = 2(-1) – 8 = -10

so your two values here would be x = -1 and y = -10

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hello Nicole!

In order to solve this problem we must first take one equation and isolate one variable. This is done below:

8x - 2y = 12 subtract 8x from both sides of the equation

-2y = 12 - 8x divide the entire equation by -2 to isolate the variable y

y = -6 + 4x

With this equation we can substitute the y variable in -4x + 2y = -16 with what we just found y to be. This would look something like this:

-4x + 2(-6 + 4x) = -16

From here we can distribute the 2 to get rid of the parenthesis

-4x -12 + 8x = -16 And now we can combine like terms to solve for x

4x = -4

We want to find out what x is by itself, so we divide each side by 4

x = -1

Great! we have one variable and we can choose either equation to solve for the other variable. All we need to do is plug in -1 instead of x, multiply, and then combine like terms in order for us to get an equation that gives us the value of y. Since we used the second equation to find x, why don't we go back to the first equation to give us y.

-4x + 2y = -16

-4(-1) + 2y = -16 Substitute x for -1

4 + 2y = -16 Multiply -4 and -1

2y = -20 Subtract both sides by -4 in order to combine like terms

y = -10 Divide both sides by 2 in order to isolate y

We can check that we are correct by plugging in out variables into either equation. Let's choose the second equation for this.

8x - 2y = 12

8(-1) - 2(-10) = 12 We know x = -1 and y = -10 so substitute the variables

-8 - (-20) = 12 Multiply where we can

-8 + 20 = 12 A minus - a minus equals a positive so we simplify

12 = 12 Correct! so we know that the two variables are correct.