How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x + y = 4# and #–x + y = 2#?

1 Answer
Mar 13, 2016

Answer:

The equations are consistent.
The point of intersection is #(x,y)->(1,3)#

Explanation:

Given:
#x+y=4#.........................(1)
#-x+y=2#.....................(2)

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Both equations are in the same format. AS such and the fact that the coefficients of #x# (which is 1 and -1) are opposite signs then at some point the will coincide. Thus there exists a single pair of coordinates that will satisfy both equations. Consequently they are consistent.

By sight: Directly adding equations (1) and (2) gives:

#2y=6#

Thus #y=3#

Given that #y=3#, by sight, #x=1#
So the graphs intersect at #(x,y)->(1,3)#

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To graph these write the equations as:
#y=-x+4# .............................(1_a)
#y=x+2#....................................(2_a)

If this is for homework you will be required to produce a table of values for each equation. I would suggest 3 values each
Tony B