How do you solve the following system?:  x + 2y = -2 , y=2x+9

Mar 18, 2018

Substitution Property

$x = - 4 \mathmr{and} y = 1$

Explanation:

If $x =$a value, then $x$ will equal that same value no matter where it is or what it's being multiplied by.

Allow me to explain.

$x + 2 y = - 2$

$y = 2 x + 9$

Replacing $y = 2 x + 9$

$x + 2 \left(2 x + 9\right) = - 2$

Distribute:

$x + 4 x + 18 = - 2$

Simplify:

$5 x = - 20$

$x = - 4$

Since we know what $x$ is equal to, we can now solve for the $y$ value using this same philosophy.

$x = - 4$

$x + 2 y = - 2$

$\left(- 4\right) + 2 y = - 2$

Simplify

$2 y = 2$

$y = 1$

$x = - 4 , y = 1$

Also, just as a general rule of thumb, if you're unsure of your answers in any system of equations like this, you can check your answers by plugging both x and y into both equations and seeing if a valid input is spit out. Like so:

$x + 2 y = - 2$

$y = 2 x + 9$

$\left(- 4\right) + 2 \left(1\right) = - 2$

Since $- 2 i s - 2$. We've solved the system of equations correctly.

$y = 2 x + 9$

$1 = 2 \left(- 4\right) + 9$

$1 = - 8 + 9$

$1 = 1.$

Hence it is verified that $x = - 4 \mathmr{and} y = 1$