How do you solve x+y=-1 and x-y=3?

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Answer 1 · 2015-11-04T05:52:50

#color(green)(x = 1#
#color(green)(y = -2#

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

By asking us to solve, the question is indirectly asking us for the value of #x and y#

To get the value of #x#, let's ADD the two equations. Because ADDING will help us eliminate #y# with ease.

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

#x + cancel(y) + x - cancel(y) = 2#

#2x = 2#

Dividing both sides by 2, we get

#(cancel(2)x)/cancel(2) = 2/2#

#color(green)(x = 1#

Now to get the value of #y# can simply substitute this value of #x# in any of the two equations

Substituting #x = 1# in the first equation, we get

#1 + y = -1#

Transposing 1 to the right hand side, we get

# y = -1 -1#

#color(green)(y = -2#