Question

The coordinate plane shows the graphs for the following system of equations.

y
=
−
x
−
4

y
=
−
5
x
3


image

Identify the solution to this system of equations. Explain how you determined the solution.

Answer 1

The solution is the point where the two lines cross. Set the right-hand sides equal and solve:

−x − 4 = −(5/3)x
Multiply by 3: −3x − 12 = −5x
Add 5x: 2x − 12 = 0 → x = 6

Now plug x = 6 into y = −x − 4: y = −6 − 4 = −10.

So the solution (intersection) is (6, −10).