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

1 Answer
May 31, 2016

Answer:

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
enter image source here

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