How do you solve x + y = 5 and 2x + Y = 8?

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Answer 1 · 2016-01-08T04:47:42

#(3,2)#

This could be solved with either elimination or substitution. I'll use elimination, since the category is "Linear Systems with Multiplication."

Multiply the first equation by #-1#.

#-1(x+y=5)rarr-x-y=-5#

We now have the two equations:

#{(-x-y=-5),(2x+y=8):}#

Add the two equations together.

#-x+2x-y+y=-5+8#

Simplify. Notice that the #y# terms cancel, which was the point in multiplying the first equation by #-1# earlier.

#x=3#

Now, substitute #x=3# into either of the original equations.

#3+y=5#
#y=2#

This leaves us with #x=3,y=2#, or the point #(3,2)#.