Question

What is the solution to the system please help

Answer 1

`(-(50)/(13),-(12)/(13))`

Explanation:

To start, you need to find the equation of both of these lines. For the orange one, the slope can be found with the points (-5,0) and (0,-4), where there is a drop of 4 for a run of 5. This is a slope of -4/5, and a y-intercept of -4. For the purple line, you can use the points (-2,0) and (0,1), where there is a rise of 1 for a run of 2 or a slope of 1/2 and a y intercept of 1. Therefore, the two equations are:

`y=-(4)/(5)x-4`

`y=(1)/(2)x+1`

You can now set them equal to each other:

`-(4)/(5)x-4=(1)/(2)x+1`

Add 4 to both sides:

`-(4)/(5)x=(1)/(2)x+5`

Multiply both sides by 2:

`-(8)/(5)x=x+10`

Multiply both sides by 5:

`-8x=5x+50`

Subtract 5x from both sides:

`-13x=50`

Divide both sides by -13:

`x=-(50)/(13)`

`y=-(12)/(13)`

Hope this helps!