# 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?

Sep 26, 2017

see explanation

#### Explanation:

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

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

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

subtract 7x from both sides:

$- 6 y = - 7 x + 36$

...divide both sides by -6:

$y = \frac{7}{6} x - 6$

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

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

$6 y = 7 x - 36$

divide both sides by 6:

$y = \frac{7}{6} x - 6$

...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.