Solving Linear Systems by Graphing Worksheet

**Page 1**

1.

How many solutions does the system of linear inequalities - $x$ + 2$y$ ≥ 6 and $x$ - 2$y$ ≥ 4 have?

a. | finite | ||

b. | 1 | ||

c. | infinite |

Correct answer : (4)

2.

Which of the graphs represent the system of equations - 2$x$ + 3$y$ > 6 and $x$ + $y$ ≤ - 3?

a. | Graph 3 | ||

b. | Graph 1 | ||

c. | Graph 2 | ||

d. | Graph 4 |

Correct answer : (3)

3.

Choose a graph that represents the following system of inequalities.

$x$ ≥ 0

$y$ ≥ 0

4$x$ + 6$y$ ≤ 12

a. | Graph 2 | ||

b. | Graph 4 | ||

c. | Graph 1 | ||

d. | Graph 3 |

Correct answer : (3)

4.

Which of the following linear systems matches the graph?

a. | $y$ = $x$ + 2, $y$ = $\frac{1}{4}$$x$ - 3 | ||

b. | $y$ = - $x$ - 2, $y$ = $\frac{1}{4}$$x$ + 3 | ||

c. | $y$ = $x$ - 2, $y$ = $\frac{1}{4}$$x$ + 3 | ||

d. | $y$ = - $x$ + 2, $y$ = $\frac{1}{4}$$x$ - 3 |

Correct answer : (4)

5.

Find the number of solutions for the linear system.

- 2$x$ + $y$ = - 4

- 10$x$ + 5$y$ = - 20

a. | exactly one solution | ||

b. | exactly two solutions | ||

c. | infinitely many solutions | ||

d. | no solution |

Correct answer : (3)

6.

Find the number of solutions for the linear system.

$x$ + $y$ = - 4

$x$ + $y$ = - 1

a. | exactly one solution | ||

b. | no solution | ||

c. | exactly two solutions | ||

d. | infinitely many solutions |

Correct answer : (2)

7.

How many solutions do the systems of linear inequalities - $x$ + 2$y$ ≥ 6 and $x$ - 2$y$ ≥ 4 have?

a. | infinite | ||

b. | finite | ||

c. | 1 |

Correct answer : (2)

8.

Which of the graphs represents the system of equations, - 2$x$ + 3$y$ > 6 and $x$ + $y$ ≤ - 3?

a. | Graph 4 | ||

b. | Graph 1 | ||

c. | Graph 3 | ||

d. | Graph 2 |

Correct answer : (4)

9.

Choose a graph that represents the system of inequalities:

$x$ ≥ 0

$y$ ≥ 0

4$x$ + 6$y$ ≤ 12

a. | Graph 3 | ||

b. | Graph 4 | ||

c. | Graph 2 | ||

d. | Graph 1 |

Correct answer : (4)

10.

Find the number of solutions the linear system has by using the graphing method.

$x$ + 4$y$ = 1

$x$ + 4$y$ = - $\frac{1}{2}$

a. | No solution | ||

b. | Exactly one solution | ||

c. | Infinitely many solutions | ||

d. | Two solutions |

Correct answer : (1)