Integrated Math 1 / Unit 6: Systems of Equations and Inequalities
6.6 Systems of Inequalities
Notes
The solution of a linear inequality in two variables is a half-plane. Graph the boundary line, then shade the side that makes the inequality true.
- Use a dashed line for $<$ or $>$ and a solid line for $\leq$ or $\geq$.
- Test a point (like the origin) to decide which side to shade.
- A system of inequalities has a solution region where all shadings overlap.
- Example: $(1, 1)$ is a solution of $y > x - 1$ and $y \leq -x + 3$ because $1 > 0$ and $1 \leq 2$.
Practice
Which point is a solution of $y \geq 2x - 1$?
$0 \geq 2(0) - 1 = -1$ is true. The other points fail.
Which inequality is graphed with a dashed boundary line?
A strict inequality ($<$ or $>$) does not include the boundary, so it is dashed.
Which point is a solution of both $y > x - 1$ and $y \leq -x + 3$?
$(1, 1)$ gives $1 > 0$ and $1 \leq 2$, both true. The other points fail at least one.
Ready for more? Take the Unit 6 test.