Systems of Inequalities

A region rather than a point.

12 problems · about 21 minutes · A-REI.D.12

NameDate

Figure — use these to answer the problems

This is one boundary line. The solution to an inequality is everything on one side of it.

y = −x + 4

Slope-1

y-intercept4

Test point x0

Test point y0

Figure 1

Straightforward practice. Get the method working first.

5 problems

Does (0, 0) satisfy y ≤ 3x − 4? 1 yes, 0 no.
Answer
2
What is the solution to a system of inequalities?
- The region where all the shaded areas overlap.
- The point where the boundary lines cross.
For y > x + 1, solid or dashed boundary? 1 solid, 2 dashed.
Answer
For y ≤ 4x, solid or dashed? 1 or 2.
Answer
Does (0, 0) satisfy y > x + 3? 1 yes, 0 no.
Answer

The same ideas with more to keep track of.

3 problems

Does (0, 0) satisfy y < 5 − x? 1 yes, 0 no.
Answer
Does (2, 3) satisfy y ≥ x? 1 yes, 0 no.
Answer
How many inequalities must a solution point satisfy in a system of three?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Put the graphing steps in order.
Write 1 to 4 in the boxes to put these in order.
- Graph the boundary line.
- Make it solid or dashed based on the symbol.
- Test a point not on the line.
- Shade the side that satisfies the inequality.
Does (1, 1) satisfy y < 2x? 1 yes, 0 no.
Answer
The Test
Does the origin satisfy y < 2x + 1? 1 yes, 0 no.
Answer
The Line
For y ≥ 3x − 2, is the boundary line solid or dashed? 1 solid, 2 dashed.
Answer