Question

What is the solution of the system when just looking at the equations? No Graph!

Example 4:
y = 5x + 2 y = 5x – 8
m = _____ m = _____
b = ______ b = ______
When comparing equations:
1. Put in _________________ form.
2. Compare the _______________!
This system has _______________________________________ solution.

Answer 1

The slope-intercept form: y = mx + b

m - slope

b - y-intercept

y = 5x + 2 and y = 5x – 8

m = 5 m = 5

b = 2 b = -8

When comparing equations:

1. Put in slope-intercept form.

2. Compare the slopes and the y-intercepts!

This system has no solution.

Because we have the same slopes and different y-intercepts.

If the slopes are the same and the y-intercepts are the same, then that system has infinitely many solutions.

If the slopes are different, then that system has one solution.