Question

What is the solution to the system please help

Answer 1

Answer:

$(-\frac{50}{13},-\frac{12}{13})$

Step-by-step 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:

$y=-\frac{4}{5}x-4$

$y=\frac{1}{2}x+1$

You can now set them equal to each other:

$-\frac{4}{5}x-4=\frac{1}{2}x+1$

Add 4 to both sides:

$-\frac{4}{5}x=\frac{1}{2}x+5$

Multiply both sides by 2:

$-\frac{8}{5}x=x+10$

Multiply both sides by 5:

$-8x=5x+50$

Subtract 5x from both sides:

$-13x=50$

Divide both sides by -13:

$x=-\frac{50}{13}$

$y=-\frac{12}{13}$

Hope this helps!