Algebra 1 Systems Inequalities Quiz – Free PDF

Contents

This algebra 1 systems inequalities quiz asks 10 multiple-choice questions on graphing linear inequalities and systems of inequalities, and each answer comes with a short explanation.

Take this ten-question quiz to check your skills with linear inequalities, solid and dashed lines, shading, and systems of inequalities. Each question has exactly one correct answer. Read each explanation, especially for the questions you miss.

Algebra 1Common Core: A-REI.D.12 · A-CED.A.3

🎯 Graphing Linear Inequalities and Systems of Inequalities – Algebra 1 math quiz

Score: 0 / 10

Answered: 0 / 10

Question 1

Which inequality is graphed?

A shaded half-plane.

A y < x + 1

B y ≥ x + 1

C y > x − 1

D y > x + 1

Question 2

Which point is a solution of $y\le 2x-1$?

A (0, 0)

B (2, 4)

C (1, 2)

D (1, 1)

Question 3

Which describes the graph of $x+y<5$?

A Dashed boundary, shaded toward the origin

B Solid boundary, shaded toward the origin

C Dashed boundary, shaded away from the origin

D Solid boundary, shaded away from the origin

Question 4

Solve $-2y>8x-6$ for $y$.

A y > −4x + 3

B y < 4x − 3

C y < −4x + 3

D y > 4x − 3

Question 5

Which point is a solution of the system whose graph is shown?

The overlap is the solution region.

A (4, 1)

B (2, 2)

C (1, −1)

D (3, 3)

Question 6

Which statement is true about $y>x+2$ and $y<x-3$?

A Every point above both lines works

B No point satisfies both inequalities

C Only the crossing point works

D Every point between the lines works

Question 7

A student buys $x$ folders at $\$2$ and $y$ pens at $\$3$ with at most $\$30$. Which inequality models the cost?

A 2x + 3y ≥ 30

B 2x + 3y < 30

C 2x + 3y ≤ 30

D 3x + 2y ≤ 30

Question 8

Which inequality is graphed?

A shaded half-plane.

A x ≥ 3

B x ≤ 3

C x < 3

D y ≤ 3

Question 9

The point $(4, 2)$ lies on the boundary of $x-2y\ge 0$. Is it a solution?

A Yes, because 0 ≥ 0 is true

B No, because 0 > 0 is false

C No, because boundary points are never solutions

D Yes, because the point is above the line

Question 10

Which are the corners of the region $x\ge 0$, $y\ge 0$ and $x+y\le 6$?

The shaded region and its corners.

A (0, 0), (6, 0), (0, 6)

B (0, 0), (6, 0), (6, 6)

C (0, 0), (3, 3), (6, 0)

D (6, 0), (0, 6), (6, 6)

🎉 Quiz complete!

0 / 10

How does this quiz work?

Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.

What should you review before the quiz?

Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.

Remember:

Standards A-REI.D.12 and A-CED.A.3: graph linear inequalities and systems, and model constraints.
Solid line for $\le$ and $\ge$; dashed line for $<$ and $>$.
Use a test point not on the line, such as $(0, 0)$, to decide which side to shade.
Multiplying or dividing by a negative number reverses the inequality symbol.
The solution set of a system is the overlap of the half-planes; a feasible region lists all allowed combinations.