correctly answer and provide explanation

A student solves the system of equations given below. In which line is an error first made?

2x -­ y = 6
2x + y = 10

Line 1 2x -­ y = 6
– ­2x + y = ­10
Line 2 0 = ­4
Line 3 0 ≠-4 so there is no solution

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a. Line 1

b. Line 2

c. Line 3

d. There is no error

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Which of the following situations would give you a system of equations that have at least 2 solutions?

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a.Two lines are parallel and have different y­-intercepts.

b. Two lines have the same slope and both pass through the origin.

c. Two lines are perpendicular and have the same y-intercept.

d. Two lines have negative slopes and different y­-intercepts.

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What is the best estimate for the solution to the system of equations shown on the graph below?

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a. (2, 3)

b. (3, 2)

c. (2.5, 3.5)

d. (3.5, 2.5)

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Solve the system of equations.

3x = ­-31 + 2y
5x + 6y = 23

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a. x = ­-5, y = 8

b. x = ­- 29, y = ­- 28

c. no solution

d. infinite solutions

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Solve the system of equations.

6d + 3f = 12

2d = 8 ­- f

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a. d= 3, f = 2

b. d = 3, f = 14

c. no solution

d. infinite solutions

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Which of the following systems is consistent and dependent?

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a. y = x + 4; y = x -­ 4

b. x + y = 4; 2x + 2y = 6

c. 3x + y = 3; 2y = 6x + 6

d. 4x ­- 2y = 6; 6x -­ 3y = 9

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Which graph shows a system of equations with no solution?

A.	B.
C.	D.

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The caterer at a brunch bought several pounds of chicken salad and several pounds of tuna salad. The chicken salad cost $9 per pound, and the tuna salad cost $6 per pound. He bought a total of 14 pounds of salad and paid a total of $111. How much chicken salad did he

buy?

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a. 6 pounds

b. 7 pounds

c. 8 pounds

d. 9 pounds

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In order to practice at home, Tadeo purchased a basketball and a volleyball that cost a total of $67, not including tax. If the price of the basketball b is $4 more than twice the cost of the volleyball v. Which system of linear equations could be used to determine the price of each ball?

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a. b + v = 67; b = 2v ­- 4

b. b + v = 67; b = 2v + 4

c. b + v = 4; b = 2v ­- 67

d. b + v = 4; b = 2v + 67

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Which of the following best describes the graph of the equations?

4y = 3x + 8
-6x = ­-8y + 24

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a. The lines are parallel

b. The lines have the same x­-intercept

c. The lines are perpendicular

d. The lines have the same y­-intercept

 

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