# 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?

Feb 14, 2018

The equations are consistent with a single solution $\left(x , y\right) = \left(4 , 7\right)$

#### 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 $\left(x , y\right)$ 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:

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

If we combine these graphs on the same plane:

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