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

1 Answer
Mar 18, 2018

Answer:

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#