Solving Linear Systems (using Substitution Method) Worksheet

**Page 1**

1.

Which of the following ordered pairs satisfies the linear system?

$x$ - $y$ = 6 [Equation 1]

2$x$ + 5$y$ = -9 [Equation 2]

$x$ - $y$ = 6 [Equation 1]

2$x$ + 5$y$ = -9 [Equation 2]

a. | (-3, -3) | ||

b. | (3, 3) | ||

c. | (-3, 3) | ||

d. | (3, -3) |

[Rearrange Equation 1.]

2

[Substitute

7

[Combine like terms.]

7

[Add 30 to each side.]

[Divide each side by 7.]

[Substitute

[Simplify.]

The solution for the linear system is (3, -3).

Correct answer : (4)

2.

Which of the following ordered pairs satisfies the linear system?

3$x$ - $y$ = 0 [Equation 1]

$x$ - 3$y$ = 0 [Equation 2]

3$x$ - $y$ = 0 [Equation 1]

$x$ - 3$y$ = 0 [Equation 2]

a. | (3, -3) | ||

b. | (-3, 3) | ||

c. | (0, 0) | ||

d. | (3, 3) |

[Rearrange Equation 1.]

[Substitute

-8

[Combine like terms.]

[Divide each side by -8.]

[Substitute

[Simplify.]

The solution for the linear system is (0, 0).

Correct answer : (3)

3.

A shopkeeper sold 60 softballs and basketballs last week for a total sum of $516. The price of a softball was $8 and that of a basketball was $20. How many softballs and basketballs did the shopkeeper sell?

a. | 56 softballs, 4 basketballs | ||

b. | 4 softballs, 57 basketballs | ||

c. | 57 softballs, 3 basketballs | ||

d. | None of the above |

[Equation 1.]

8

[Equation 2.]

[Revise Equation 1.]

8(-

[Substitute

12

[Combine like terms.]

12

[Subtract 480 from each side.]

[Divide each side by 12.]

[Substitute

The shopkeeper sold 57 softballs and 3 basketballs.

Correct answer : (3)

4.

The price of each marble was $4 and the price of each dice was $2. A total of 90 marbles and dice were purchased for $262. Find the number of marbles and the number of dice purchased.

a. | 41 marbles, 49 dice | ||

b. | 37 marbles, 53 dice | ||

c. | 39 marbles, 51 dice | ||

d. | 43 marbles, 47 dice |

[Equation 1.]

4

[Equation 2.]

[Rearrange Equation 1.]

4(90 -

[Substitute

-2

[Combine like terms.]

-2

[Subtract 360 from each side.]

[Divide each side by -2.]

[Substitute

41 marbles and 49 dice are purchased.

Correct answer : (1)

5.

Which of the following linear systems has the solution (3, 0)?

a. | x + 3y = -3 and x + 4y = -3 | ||

b. | x - 3y = -3 and x + 4y = 3 | ||

c. | -x + 3y = 3 and x - 4y = 3 | ||

d. | x + 3y = 3 and x - 4y = 3 |

3 + 3(0) = 3 + 0 = 3

For the linear system

[Substitute (3, 0) in

3 - 4(0) = 3 - 0 = 3

[Substitute (3, 0) in

So, the linear system in the choice D has the solution (3, 0).

Correct answer : (4)

6.

Which of the following equations would you use to isolate the variable?

6$x$ + 9$y$ =1 [Equation 1]

$x$ - 5$y$ = -4 [Equation 2]

6$x$ + 9$y$ =1 [Equation 1]

$x$ - 5$y$ = -4 [Equation 2]

a. | Equation 1 | ||

b. | Equation 2 |

So, Equation 2 can be used for isolating the variable.

Correct answer : (2)

7.

Which of the following equations would you use to isolate the variable?

-5$x$ + $y$ = 14 [Equation 1]

3$x$ + 2$y$ = 8 [Equation 2]

-5$x$ + $y$ = 14 [Equation 1]

3$x$ + 2$y$ = 8 [Equation 2]

a. | Equation 1 | ||

b. | Equation 2 |

So, Equation 1 can be used for isolating the variable.

Correct answer : (1)

8.

Which of the following ordered pairs satisfies the linear system?

2$x$ - 2$y$ = 2 [Equation 1.]

-$x$ + 5$y$ = -37 [Equation 2.]

-$x$ + 5$y$ = -37 [Equation 2.]

a. | (-8, 9) | ||

b. | (-9, 9) | ||

c. | (-8, -9) | ||

d. | (-9, -9) |

[Original equation 2.]

[Revise equation 2.]

2(37 + 5

[Substitute 37 + 5

8

[Combine like terms.]

8

[Subtract 74 from each side.]

[Divide each side by 8.]

[Substitute -9 for

[Simplify.]

The solution for the linear system is (-8, -9).

Correct answer : (3)

9.

Lindsay purchased a total of 42 books and toys for the Ashton play school. Each book cost $11 and each toy cost $6. How many books and toys did she buy for $367?

a. | 19 books and 23 toys | ||

b. | 22 books and 20 toys | ||

c. | 23 books and 19 toys | ||

d. | 20 books and 22 toys |

[Linear equation for the total books and toys.]

11

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

11

[From equation 1,

5

[Combine like terms.]

5

[Subtract 252 from each side.]

[Divide each side by 5.]

[Substitute

Lindsay bought 23 books and 19 toys.

Correct answer : (3)

10.

Tony purchased 24 pens and markers for $128. The price of a marker was $9 and the price of a pen was $5. How many pens and markers did Tony buy?

a. | 22 markers, 2 pens | ||

b. | 21 markers, 3 pens | ||

c. | 2 markers, 22 pens | ||

d. | 1 markers, 23 pens |

[Equation 1.]

9

[Equation 2.]

[Revise Equation 1.]

9

[Substitute

4

[Combine like terms.]

4

[Subtract 120 from each side.]

[Divide each side by 4.]

[Substitute

Tony bought 2 markers and 22 pens.

Correct answer : (3)