Solving Linear Systems by Substitution Answers

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What is the value of x in the solution to the system of linear equations?

Question illustration
A
–7
B
–3
C
1
D
5
2
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Package A contains 3 birthday cards and 2 thank-you notes and costs $9.60. Package B contains 8 birthday cards and 6 thank-you notes and costs $26.60. If x represents the cost of a birthday card and y represents the cost of a thank-you note, how much does each birthday card cost?

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A
$1.33
B
$1.50
C
$2.20
D
$3.10
3

A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy each basic model and $50 to buy each upgraded model from the phone company. On Tuesday, the store has $1,800 in sales for these two models, and it paid the phone company $400 to buy these phones. How many upgraded models did the store sell on Tuesday?

A
6 upgraded phones
B
10 upgraded phones
C
15 upgraded phones
D
42 upgraded phones
4

What is the solution to the system of equations?

Question illustration
A
(4, 7)
B
(7, 4)
C
(12, 5)
D
(5, 12)
5

Which statement describes the system of equations?

Question illustration
A
It has infinitely many solutions.
B
It has no solution.
C
It has one solution (0, 1).
D
It has one solution (4, –1).
6

Mira is playing a game where she is trying to toss a ball into a large basket or a small basket. The large basket is worth 2 points, and the small basket is worth 3 points. Mira made 15 baskets for a total of 35 points. If x represents the number of large baskets made and y represents the number of small baskets made, how many large baskets did she make?

Question illustration
A
2 large baskets
B
5 large baskets
C
7 large baskets
D
10 large baskets
7

What is the solution to the following system of equations?

Question illustration
A
It has infinitely many solutions.
B
It has no solution.
C
It has one solution (2, –3).
D
It has one solution (4, 0).
8

Which first step for solving the given system using substitution results in an equation without fractions?

Question illustration
A
Solve for x in the first equation.
B
Solve for y in the first equation.
C
Solve for x in the second equation.
D
Solve for y in the second equation.
9

What is the solution to the system of equations?

Question illustration
A
(7, 9)
B
(9, 7)
C
(–5, 11)
D
(11, –5)
10

Which first step for solving the given system using substitution results in an equation without fractions?

Question illustration
A
Solve for x in the first equation.
B
Solve for y in the first equation.
C
Solve for x in the second equation.
D
Solve for y in the second equation.

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