Question

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

Answer 1

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)) :}#

`color(white)("XXX")`(it took a bit of testing of `x` values to get the second `y` value that was an integer for `9x-9y=-56`)

Plot and Draw the Lines for Each Equation

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