Algebra 1 / Unit 6: Systems of Equations and Inequalities
6.5 Systems of Linear Inequalities
Notes
The solution of a system of inequalities is the region where all the shaded areas overlap.
- Graph each boundary line: solid for $\le$ or $\ge$, dashed for $<$ or $>$.
- Shade the side that makes the inequality true. Test a point like $(0, 0)$ if it isn't on the line.
- Any point in the overlap is a solution.
Practice
Which point is a solution of $y > x$ and $y < 4$?
$3 > 1$ and $3 < 4$.
The boundary line of $y \ge -2x + 1$ is drawn:
$\ge$ includes the line, and greater $y$ means above.
A student can work at most 20 hours a week and needs to earn at least $180 at $12 per hour. Which system fits hours $h$?
At most 20 hours, at least $180 earned.
Ready for more? Take the Unit 6 test.