How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x+y=11#, #x-y=-3#?

1 Answer
Alan P.
Feb 14, 2018

The equations are consistent with a single solution #(x,y)=(4,7)#

Explanation:

Using graphing (as requested)

We can be picking arbitrary values for #x# using the equation #x+y=11# we can generate a few (two would actually be enough, but I generated 3 for demonstration purposes) solution points for #(x,y)# on this line:
#color(white)("XXX"){:(ul(x),color(white)("xx"),ul(y)), (0,,11),(5,,6),(11,,0) :}#
Plotting these sample points on the plane and drawing a line through the points, we get a graph of the form:
enter image source here

We can repeat this process for #x-y=-3#.
The sample solution points that I generated for this were
#color(white)("XXX"){:(ul(x),color(white)("xx"),ul(y)), (0,,3),(5,,8),(-3,,0) :}#
to generate the graph

enter image source here

If we combine these graphs on the same plane:
enter image source here

We see that the two lines intersect (and therefore are consistent)
at the coordinates #(x,y)=(4,7)#

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