Question

Solve each system by graphing. -5x-20y=-152x+8y=6

Answer 1

To answer this question, we need to rewrite the equations into the slope-intercept form of the line:

$y=mx+b$

Then, we have the first equation:

$-5x-20y=-15\Rightarrow5x+20y=15\Rightarrow20y=15-5x$

Then, we have:

$\frac{20}{20}y=\frac{15}{20}-\frac{5}{20}x\Rightarrow y=\frac{3}{4}-\frac{1}{4}x\Rightarrow y=-\frac{1}{4}x+\frac{3}{4}$

For the second equation, we have:

$2x+8y=6\Rightarrow8y=6-2x\Rightarrow\frac{8y}{8}=\frac{6}{8}-\frac{2}{8}x\Rightarrow y=\frac{3}{4}-\frac{1}{4}x\Rightarrow y=-\frac{1}{4}x+\frac{3}{4}$

As we can see, both lines have the same equation. It means that if we graph both lines, the graph of both equations will be the same.

Let us find the x-intercept and the y-intercept of the lines (they are the same for both cases.)

The x-intercept

The x-intercept is the point for the line when y = 0. Then, when y = 0, we have:

$y=-\frac{1}{4}x+\frac{3}{4}\Rightarrow0=-\frac{1}{4}x+\frac{3}{4}\Rightarrow\frac{1}{4}x=\frac{3}{4}$

If we multiply by 4 to both sides of the equation, we have:

$4\cdot\frac{1}{4}x=4\cdot\frac{3}{4}\Rightarrow x=3$

Then, the x-intercept is x = 3, y = 0 or (3, 0).

The y-intercept