Question

Which graph shows the solution to the following system? y= 1/4x - 2
y = 7/4x + 4

Answer 1

These two lines will intersect at (-4, -3). The top equation will have a slope of 1/4 and the bottom one a slope of 7/4. Paste them in Wolfram Alpha to see the pic:

 

Answer 2

Answer with explanation:

The equation of two lines are

    $1. y=\frac{x}{4}-2\\\\2. y=\frac{7 x}{4}+4$

Slope of both the lines are different.Also

  $\frac{\frac{1}{4}}{\frac{7}{4}}\neq \frac{1}{1}\neq \frac{-2}{4}$

It means lines will intersect at a point.

$x -4y=8\\\\7 x -4 y= -16\\\\ x - 7 x- 4 y+4 y=8+16\\\\ -6 x =24\\\\ x=\frac{-24}{6}=-4\\\\-4-4 y=8\\\\-4 y=12\\\\y=\frac{12}{-4}\\\\y=-3$

Plotting the graph of both the linear equation, and get solution of the system of equation is

x= -4,and , y= -3