Linear Systems Worksheet

**Page 1**

1.

The cost of an apple is $1 and that of an orange is $0.4. Gary purchased 18 fruits for $15. If A represents the number of apples and O the number of oranges, which system of linear equations represents the situation?

a. | A + O = 15 and A + 0.4O = 18 | ||

b. | A + O = 15 and 0.4A + O = 18 | ||

c. | A + O = 18 and 0.4A + O = 15 | ||

d. | A + O = 18 and A + 0.4O = 15 |

[Total number of fruits = 18.]

Cost of A apples is $A.

[Cost of an apple = $1.]

Cost of O oranges is $0.4O.

[Cost of an orange = $0.4.]

Cost of 18 fruits is $15, so A + 0.4O = 15

[Total cost = $15.]

So, the system of equations are A + O = 18 and A + 0.4O = 15

Correct answer : (4)

2.

Choose the easiest method to solve the linear system.

5$x$ + $y$ = 6

- 6$x$ - 4$y$ = 4

a. | linear combination method | ||

b. | substitution method |

You can solve Equation 1 for

Correct answer : (2)

3.

Choose the easiest method to solve the linear system.

Correct answer : (0)

4.

Choose the easiest method to solve the linear system.

5$x$ + 2$y$ = 16

$x$ - 4$y$ = - 10

a. | substitution method | ||

b. | linear combination method |

You can solve Equation 2 for

Correct answer : (1)

5.

Choose the best method to solve the linear system.

- 8$x$ + 3$y$ = 5

11$x$ - 5$y$ = - 16

a. | substitution method | ||

b. | linear combination method |

Correct answer : (2)

6.

Jim bought two types of movie tickets at $4 and $5 for 8 of his friends. Total cost of the tickets is $37. Let $x$ be the number of $4 tickets and $y$ be the number of $5 tickets. Which system of linear equations represents the situation?

a. | $x$ + $y$ = 37 and 4$x$ + 5$y$ = 8 | ||

b. | $x$ + $y$ = 8 and 5$x$ + 4$y$ = 37 | ||

c. | 4$x$ + 5$y$ = 37 | ||

d. | $x$ + $y$ = 8 and 4$x$ + 5$y$ = 37 |

[Total number of tickets = 8.]

Cost of

Cost of

4

[total ticket cost is $37.]

So, the system of equations are

Correct answer : (4)

7.

A shopkeeper sold 36 softballs and basketballs for a sum of $396. The price of a softball is $9 and that of a basketball is $27. How many softballs and basketballs did the shopkeeper sell?

a. | 5 softballs, 32 basketballs | ||

b. | 32 softballs, 4 basketballs | ||

c. | 36 softballs, 5 basketballs | ||

d. | 9 softballs, 32 basketballs |

[Equation 1.]

9

[Equation 2.]

[Revise Equation 1.]

9(-

[Substitute

18

[Combine like terms.]

18

[Subtract 324 from each side.]

[Divide each side by 18.]

[Substitute

The shopkeeper sold 32 softballs and 4 basketballs.

Correct answer : (2)

8.

Ed purchased 28 pens and markers for $88. The price of a marker is $5 and the price of a pen is $3. How many pens and markers did Ed buy?

a. | 25 markers, 3 pens | ||

b. | 26 markers, 2 pens | ||

c. | 2 markers, 26 pens | ||

d. | 6 markers, 27 pens |

[Equation 1.]

5

[Equation 2.]

[Revise Equation 1.]

5

[Substitute

2

[Combine like terms.]

2

[Subtract 84 from each side.]

[Divide each side by 2.]

[Substitute

Ed bought 2 markers and 26 pens.

Correct answer : (3)

9.

The price of each marble is $7 and the price of each dice is $5. A total of 34 marbles and dice were purchased for $202. Find the number of marbles and the number of dice purchased.

a. | 16 marbles, 18 dice | ||

b. | 18 marbles, 16 dice | ||

c. | 14 marbles, 20 dice | ||

d. | 12 marbles, 22 dice |

[Equation 1.]

7

[Equation 2.]

[Rearrange Equation 1.]

7(34 -

[Substitute

- 2

[Combine like terms.]

- 2

[Subtract 238 from each side.]

[Divide each side by -2.]

[Substitute

16 marbles and 18 dice are purchased.

Correct answer : (1)

10.

Valerie purchased a total of 18 books and toys for the Dugway play school. Each book costs $23 and each toy costs $12. How many books and toys did she buy for $337?

a. | 11 books and 7 toys | ||

b. | 10 books and 8 toys | ||

c. | 7 books and 11 toys | ||

d. | 8 books and 10 toys |

[Linear equation for the total books and toys.]

23

[Equation for the total cost of the books and toys.]

23

[From equation 1,

11

[Combine like terms.]

11

[Subtract 216 from each side.]

[Divide each side by 11.]

[Substitute

Valerie bought 11 books and 7 toys.

Correct answer : (1)