Question

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

Answer 1

Substitution Property

`x=-4 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 + 2y = -2`

`y = 2x + 9`

Replacing `y=2x+9`

`x + 2(2x + 9) = -2`

Distribute:

`x + 4x + 18 = -2`

Simplify:

`5x = -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 + 2y = -2`

`(-4) + 2y = -2`

Simplify

`2y = 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 + 2y = -2`

`y = 2x + 9`

`(-4) + 2(1) = -2`

Since `-2 is -2`. We've solved the system of equations correctly.

`y = 2x + 9`

`1 = 2(-4) + 9`

`1 = -8 + 9`

`1 = 1.`

Hence it is verified that `x=-4 and y =1`