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:

`(20)/(20)y=(15)/(20)-(5)/(20)x\Rightarrow y=(3)/(4)-(1)/(4)x\Rightarrow y=-(1)/(4)x+(3)/(4)`

For the second equation, we have:

`2x+8y=6\Rightarrow8y=6-2x\Rightarrow(8y)/(8)=(6)/(8)-(2)/(8)x\Rightarrow y=(3)/(4)-(1)/(4)x\Rightarrow y=-(1)/(4)x+(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=-(1)/(4)x+(3)/(4)\Rightarrow0=-(1)/(4)x+(3)/(4)\Rightarrow(1)/(4)x=(3)/(4)`

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

`4\cdot(1)/(4)x=4\cdot(3)/(4)\Rightarrow x=3`

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

The y-intercept