4. Solving Linear Systems
Sign In
Start by expressing the lines in slope-intercept form. What information can you obtain?
See solution.
y=mx+b In the above formula, m is the slope and b is the y-intercept of the line. Let's see how these two things are useful to determine the number of solutions.
| Condition | Example | Number of Solutions |
|---|---|---|
| The lines have different slopes. | y=2x+4 y=- 3x+2 | One solution. |
| The lines have the same slope and the same y-intercept. | y=5x+1 y=5x+1 | Infinitely many solutions. |
| The lines have the same slope but different y-intercept. | y=- x-2 y=- x+7 | No solution. |