How do you find the solution of the system of equations #x-2y=2# and #y= -1/2x-5#?

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Answer 1 · 2018-06-15T07:37:27

#x = -4#
#y = -3#

The second equation gives an expression for #y# in terms of #x#:

#y = -1/2x - 5#

This means that we can substitute the #y# in the first equation with that expression:

#x-2color(red)(y)=2 \to x-2\color(red)((-1/2x - 5))=2#

Rearrange this last expression:

#x+x+10=2 \to 2x+10=2#

Subtract #10# from both sides:

#2x = -8#

Divide both sides by #2#:

#x = -4#

Now that we know #x#, we can use the expression for #y# to find it out:

#y = -1/2\color(red)(x) - 5 = -1/2\color(red)((-4)) - 5 = 2-5 = -3#