Question

Solve this system of equations by graphing. First graph the equations, and then type the solution.
y=3x+1
y=x–3
describe exact points to plot for both equations.

Answer 1

To graph each line, plot two (or three) exact points and draw the straight line through them.

For y = 3x + 1
- y-intercept: x = 0 → (0, 1)
- another point: x = 1 → (1, 4)
(You can also plot x = -2 → (-2, -5), which will be the intersection.)

For y = x − 3
- y-intercept: x = 0 → (0, −3)
- another point: x = 3 → (3, 0)
(Again x = -2 → (-2, −5) lies on this line too.)

Graph each line through its points. The lines meet at (-2, −5).

Check:
3(−2)+1 = −6+1 = −5 and (−2)−3 = −5, so the solution is
(-2, -5).