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

Question

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

Nathan Axel · Accepted Answer

Substitution Property

#x=-4 and y =1# If #x = #a value, then #x# will equal that same value no matter where it is or what it's being multiplied by. Let me clarify. #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# As a general rule of thumb, you can verify your answers in any system of equations similar to this one by entering both x and y into both equations and observing whether a valid input is returned. For example: #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#

Kennedy Adams · Answer

undefined To solve the system of equations $x + 2y = -2$ and $y = 2x + 9$, you can use substitution or elimination method. Here's how to do it using the substitution method:

1. Substitute $y$ in the first equation with the expression from the second equation:
   $$ x + 2(2x + 9) = -2 $$

2. Simplify the equation:
   $$ x + 4x + 18 = -2 $$
   $$ 5x + 18 = -2 $$
   $$ 5x = -20 $$
   $$ x = -4 $$

3. Substitute the value of $x$ back into the second equation to find $y$:
   $$ y = 2(-4) + 9 $$
   $$ y = -8 + 9 $$
   $$ y = 1 $$

So, the solution to the system of equations is $x = -4$ and $y = 1$.