Practice Constraint System in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A collection of equations and inequalities that must ALL be satisfied simultaneously by the same set of variable values.

Multiple conditions at once: ' $x > 0$ AND $x + y = 10$ AND $y \leq 6$ .'

Showing a random 20 of 50 problems.

Example 1

easy

What is the only integer satisfying both

x \ge 5

and

x \le 5

Example 2

easy

x + y = 8

and

x = 5

, find

y

Example 3

hard

Find

k

so that

x + y = 5

and

2x + 2y = k

have infinitely many solutions.

Example 4

challenge

For what value of

k

does the system

x+y=4

2x+2y=k

have infinitely many solutions?

Example 5

hard

A shop sells notebooks for \$3 and pens for \$1. You have \$12 and want at least 2 notebooks. How many pens can you buy?

Example 6

challenge

Find all

(x,y)

with

x,y\ge0

integers and

2x+3y=12

Example 7

medium

Solve the system

x+y=10

x-y=4

Example 8

easy

Which integer satisfies both

x\ge 2

and

x\le 2

Example 9

medium

Solve the system

x + y = 11

x - y = 3

Example 10

medium

Solve the system

x+2y=7

3x-2y=5

Example 11

easy

Does

x = 0

satisfy

x > 0

and

x < 4

Example 12

medium

Find

(x, y)

with

x \ge 0

y \ge 0

, and

x + y = 7

that maximizes

x

Example 13

medium

Find all integers

x

with

x>0

x\le 6

, and

x

even.

Example 14

medium

Solve

3x + 4y = 20

and

x = 4

Example 15

easy

List integers

x

satisfying

x \ge 3

and

x \le 6

Example 16

medium

Find integers with

x\ge 1

x\le 5

, and

x

odd.

Example 17

easy

x+y=5

and

x=2

, find

y

Example 18

medium

Solve

x-y=1

and

x+y=7

Example 19

easy

Does

x=4

satisfy both

x>0

and

x<10

Example 20

medium

Solve

2x + y = 9

and

x - y = 0

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Related Concepts

Systems of Equations Inequalities Linear Programming