Question

What do the following two equations represent? -4x-4y = -5 12x+12y = 112x

Answer 1

Answer:

These two lines are parallel and system of these equations have no solution

Step-by-step explanation:

Parallel Lines: Lines having same slope and different x and y intercept are parallel lines. System of such equations does not have any solution as these lines does not intersect at any finite points.

Standard form of line is $y=mx+c$ where $m$ is slope and $c$ is y-intercept.

First Line:

$-4x-4y=-5\\\\-4y=-5+4x\\\\Divide\ both\ sides\ by\ -4\\\\y=-x+\frac{5}{4}\\\\compare\ with\ y=mx+c\\\\slope=-1,\ c=\frac{5}{4}$

Second Line:

$12x+12y=112\\\\12y=112+-12x\\\\Divide\ both\ sides\ by\ 12\\\\y=-x+\frac{12}{112}\\\\compare\ with\ y=mx+c\\\\slope=-1,\ c=\frac{12}{112}$

Hence these two lines are parallel and system of these equations have no solution