Question

Consider the system of equations.

y
=
1
3
x
−
8

y
=
−
5
3
x
−
2


Identify the solution to the system of equations. Explain how the graph shows this solution.

image

Answer 1

Solve by setting the two expressions for y equal:

(1/3)x − 8 = (−5/3)x − 2
(1/3 + 5/3)x = −2 + 8
(6/3)x = 6 → 2x = 6 → x = 3

Then y = (1/3)(3) − 8 = 1 − 8 = −7.

So the solution is (3, −7). On the graph this is the single point where the two lines cross — the intersection point of y = (1/3)x − 8 and y = (−5/3)x − 2.