How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #7x-6y=36# and #6y-7x=-36#?

1 Answer
Sep 26, 2017

Answer:

see explanation

Explanation:

...to solve this graphically, you'll need to rewrite each of your 2 equations as the equation for a line: #y = mx+ b#.

Plot each of the lines. Your solution is the point at which they intersect. (IF they intersect.)

Eq. 1: #7x - 6y = 36#

subtract 7x from both sides:

#-6y = -7x + 36#

...divide both sides by -6:

#y = 7/6x - 6#

graph{7/6x - 6 [-10, 10, -5, 5]}

Eq. 2: #6y-7x=-36#

add 7x to each side:

#6y=7x-36#

divide both sides by 6:

#y=7/6x-6#

...which is the exact same equation, for the exact same line.

Therefore, there's no single point of intersection, and no single solution.

The question of whether the system is consistent/inconsistent may be moot - since they're both the same equation, it's not a proper system.