How do you solve #x + y = 2# and #2x + y = -1# using substitution?

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Answer 1 · 2016-03-07T02:56:44

#x = -3 and y = 5#

Since #x+y = 2#, we can say that #x = 2 - y#.

We then substitute this into the equation #2x + y = -1#.

So it becomes #2(2 - y) + y = -1#.

Open the bracket and simplify.

#4 - 2y + y = -1#

#4 - y = -1#

Add #(1+y)# to both sides of the equation and simplify.

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

#4 cancel(-y) + (1+cancel(y)) = cancel(-1) + (cancel(1)+y)#

#5 = y#

Substitute the value of #y# back in the first equation.

#x = 2 - y#

#= 2 - 5#

#= -3#

So we have #x = -3# and #y = 5#. To check your answer. Substitute both values into both equations.

#x+y = -3 + 5 = 2#

#2x+y = 2(-3) + 5 = -1#

They match.