How do you solve # 5x - y =17#, #5x +6y =3# by graphing and classify the system?

1 Answer
Sep 30, 2016

Answer:

The equations are consistent (see below for method of graphing).

Explanation:

For each equation find pairs of values for #(x,y)# that satisfy the equation. (If possible, try to find integer values since these will be easier to graph). Find at least 2 pairs for each equation (preferably 3 or more to validate the results)

#color(red)(5x-y=17)#
#color(white)("XXX"){: (color(red)(underline(x)),color(red)(underline(y))), (color(red)(4),color(red)(3)), (color(red)(3),color(red)(-2)), (color(red)(5),color(red)(8)) :}#

#color(green)(5x+6y=3)#
#color(white)("XXX"){: (color(green)(underline(x)),color(green)(underline(y))), (color(green)(3),color(green)(-2)), (color(green)(-3),color(green)(3)), (color(green)(-9),color(green)(8)) :}#

Plot each set of points on the Cartesian Plane and draw a line through the point for each set.

enter image source here

Since the lines for these equations intersect at a single point #(3,-2)# the equations are consistent.