Math Practice Problems - System of Linear Inequality Graphs

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System of Linear Inequality Graphs - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=simple

Write the inequalities that this graph represents.
Examples: y>3x/4, x≤2, y≥1, y>-2x
Then pick out which points fulfill both.
Type >= for ≥, etc.

Inequality 1:
Inequality 2:

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Inequality 1:
Inequality 2:

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Complexity=1, Mode=y=mx+b

Write the inequalities that this graph represents, which should all be in y=mx+b format.
Examples: y>2x-3, y≤-4x/3+1
Then pick out which points fulfill both.
Type >= for ≥, etc.

Complexity=2, Mode=y=mx+b

Write the inequalities that this graph represents, which should all be in y=mx+b format.
Examples: y>2x-3, y≤-4x/3+1
Then pick out which points fulfill both.
Type >= for ≥, etc.

Answers

Complexity=1, Mode=simple

Write the inequalities that this graph represents.
Examples: y>3x/4, x≤2, y≥1, y>-2x
Then pick out which points fulfill both.
Type >= for ≥, etc.

Problem

Correct Answer

Your Answer

Inequality 1:
Inequality 2:

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
Horizontal lines have a slope of 0, and are expressed in the form y=[y-intercept]
The shaded region is below the line, so we use a less than sign.
The line is dashed, so use < for less than. Any points along it are not included part of the solution.
Vertical lines have undefined slope, and are expressed in the form x=[x-intercept].
The shaded region is to the left of the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.

Problem

Correct Answer

Your Answer

Inequality 1:
Inequality 2:

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
Vertical lines have undefined slope, and are expressed in the form x=[x-intercept].
The shaded region is to the left of the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.
Vertical lines have undefined slope, and are expressed in the form x=[x-intercept].
The shaded region is to the right of the line, so we use a greater than sign.
The line is dashed, so use > for greater than. Any points along it are not included part of the solution.

Complexity=1, Mode=y=mx+b

Write the inequalities that this graph represents, which should all be in y=mx+b format.
Examples: y>2x-3, y≤-4x/3+1
Then pick out which points fulfill both.
Type >= for ≥, etc.

Problem

Correct Answer

Your Answer

Inequality 1:
Inequality 2: y <= 5x + 17

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
The first line's slope is 1
The first line's y-intercept is 1
The shaded region is below the line, so we use a less than sign.
The line is dashed, so use < for less than. Any points along it are not included part of the solution.
The second inequality is given.

Problem

Correct Answer

Your Answer

Inequality 1: y > -x/5 - 2/5
Inequality 2:
Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
The first inequality is given.
The second line's slope is -2
The second line's y-intercept is -4
The shaded region is below the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.

Complexity=2, Mode=y=mx+b

Write the inequalities that this graph represents, which should all be in y=mx+b format.
Examples: y>2x-3, y≤-4x/3+1
Then pick out which points fulfill both.
Type >= for ≥, etc.

Problem

Correct Answer

Your Answer

Inequality 1:
Inequality 2: y <= -5x - 18

Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
The first line's slope is -¹/₃
The first line's y-intercept is -4
The shaded region is below the line, so we use a less than sign.
The line is solid, so use <= for less than or equal to.
The second inequality is given.

Problem

Correct Answer

Your Answer

Inequality 1:
Inequality 2:
Which of these are part of the solution set?

(-6,6)

(-3,6)

(0,6)

(3,6)

(6,6)

(-6,3)

(-3,3)

(0,3)

(3,3)

(6,3)

(-6,0)

(-3,0)

(0,0)

(3,0)

(6,0)

(-6,-3)

(-3,-3)

(0,-3)

(3,-3)

(6,-3)

(-6,-6)

(-3,-6)

(0,-6)

(3,-6)

(6,-6)

None
of the
above

Solution
The first line's slope is -¹/₂
The first line's y-intercept is 4
The shaded region is above the line, so we use a greater than sign.
The line is dashed, so use > for greater than. Any points along it are not included part of the solution.
The second line's slope is ¹/₄
The second line's y-intercept is 4
The shaded region is below the line, so we use a less than sign.
The line is dashed, so use < for less than. Any points along it are not included part of the solution.

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