How do you solve this system of equations: #2x + y = 0 and x - 2y = - 5#?

1 Answer
Zero Two
May 14, 2018

#y = 2#
#x = -1#

Explanation:

We can solve this one of two ways; by elimination or by substitution. I don't know which one is your preferred method so I will do both. Both methods will yield the same answer.

Method 1: Elimination

  1. #2x+y =0#
  2. # x -2y = -5#

Let us use #x# as the variable we want to work out; first, you have to equate the coefficients of the #y# so equation 1 will be doubled.

  1. #4x +2y = 0#
  2. #x - 2y = -5#

Since they are opposite signs we will add the two equations so the #y# cancel out ( #2y +(-2y) = 0#), leaving only the #x# in the equation.

#5x = -5#
#x = -1#

Substitute that value of #x# into equation 1 to find the value of #y#

#4(-1) +2y = 0#

#-4+2y =0#

#2y = 4#

#y =2#

Method 2: Substitution

  1. #2x +y = 0#
  2. #x-2y = -5#

First, take one of the two equations, and make either #x# or #y# the subject.

#2x+y = 0 -> y = -2x#

Then, put that value of #y# into equation 2.

#x - 2(-2x) = -5#

Now calculate the value of #x#.

#x +4x = -5#

#5x = -5#

#x = -1#

Now put the value of #x# into the rearranged equation 1 to find the value of #y#.

#y = -2(-1)#

#y = 2#

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