How do you solve this system of equations: #2x + y = - 2 and 5x + 3y = - 8#?

1 Answer
Dr. K.
Aug 2, 2018

x = 2
y = -6

Explanation:

The question is asking to solve for 2 unknowns using 2 equations.

Let's start by rearranging one of the equation. That will make it easier to substitute. You can start with either equation, but I find the first equation easier to rearrange:
#2x + y = -2#
#2x + y color(red)( -2x) = -2 color(red)(-2x)# [move 2x to the other side]
#y = -2 -2x# [simplify]

and insert that into the second equation:
#5x + 3y = -8#
#5x + 3(color(red)(-2-2x))=-8# [substitute "-2-2x" for y]
#5x + color(red)(-6 -6x) = -8# [multiply out]
#-6 - x = -8# [simplify]
#x = 2#

Now that we have found the value for x, we can substitute in the value for x in any one of the equation to find the value for y.
#y = -2 -2x#
#y = -2 -2(2)# [substitute in the value of x]
#y = -6#

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