# How do you solve  y=-x-10, 9x-8y=-56 by graphing and classify the system?

May 31, 2016

Plot the graphs for both equations, then note if the corresponding lines intersect, are parallel, or co-linear.
(In this case they intersect and so the equations are consistent).

#### Explanation:

Find A Pair of Sample Solution Points for Each Equation

{: (,color(red)(y=-x-10),,color(white)("XXXXXXXXXX"),,color(blue)(9x-8y=-56),), (color(white)("X")color(red)(x),,color(white)("X")color(red)(y),,color(white)("X")color(blue)(x),,color(white)("X")color(blue)(y)), (color(white)("X")color(red)(0),,color(red)(-10),,color(white)("X")color(blue)(0),,color(white)("X")color(blue)(7)), (color(red)(-10),,color(white)("X")color(red)(0),,color(blue)(-8),,color(blue)(-2)) :}

$\textcolor{w h i t e}{\text{XXX}}$(it took a bit of testing of $x$ values to get the second $y$ value that was an integer for $9 x - 9 y = - 56$)

Plot and Draw the Lines for Each Equation

Note That the Lines Intersect
Since the lines intersect [at $\left(- 8 , - 2\right)$] the equations are consistent.