How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #5x-6y=-18# and #6y-5x=18#?

1 Answer
Jan 13, 2016

Answer:

Careful observation reveals that these are the same line.

Explanation:

If you take the first equation,

#5x-6y=-18#

and multiply both sides by -1, you get

#-5x+6y=18#

which rearranges to

#6y-5x=18#

Since they are the same line, ALL solutions for #x# and #y# are the same for both lines, so the system is consistent.

The easiest way to graph is to choose two values for #x#, say 0 and 10, and solve for #y#. You can then plot these points #(x,y) # and draw a line through both points.

If the lines were NOT the same, you could graph them the same way (choosing values for #x#), and finding the point where the two lines intersect.

To help you visualize what is going on, you may find it useful to play with a graphing calculator such as https://www.desmos.com/calculator.