How do you solve the system of equations by graphing #x+y=3# and #x-y=1# and then classify the system?

1 Answer
Jan 13, 2018

Answer:

This pair of equations are consistent with a single solution
#x=2#, #y=1#

Explanation:

Graphing solution (sorry I missed this requirement initially.
The graph of #x+y=3# looks like:
graph{(3-x) [-10, 10, -5, 5]}
and
the graph of #x-y=1# looks like
graph{x-1 [-12.66, 12.65, -6.33, 6.33]}

When combined we have
enter image source here
with a single point of intersection at #(x,y)=(2,1)#

Non-graphing solution
Given
[1]#color(white)("XXX")x+y=3#
[2]#color(white)("XXX")x-y=1#

adding [1] and [2] together gives
[3]#color(white)("XXX")2x=4#
which implies
[4]#color(white)("XXX")x=2#

subtracting [2] from [1] gives
[5]#color(white)("XXX")2y=2#
which implies
[6]#color(white)("XXX")y=1#

This pair of equations are consistent with a single solution
#x=2#, #y=1#