AnswersMathematics 8Linear Systems of Equations

Practice Test Answers

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1
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What was Dimitri’s mistake?

A
He mixed up the coordinates of the ordered pair when substituting it into the equations 7 x plus 9 y is equal to negative 4 and 5 x minus 2 y is equal to 6 .
B
He checked the equation 7 x plus 9 y is equal to negative 4 first when he should have checked 5 x minus 2 y is equal to 6 first.
C
He made a mistake in his calculations when substituting the ordered pair into the equation 5 x minus 2 y is equal to 6 and simplifying.
D
He made a mistake in his calculations when substituting the ordered pair into the equation 7 x plus 9 y is equal to negative 4 and simplifying.
3

Serina wants to solve the following system of equations in the most efficient way. 2 x plus 3 y is equal to 18 x plus 7 y is equal to 31 She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18 Why is Serina mistaken?

A
Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3 .
B
Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution.
C
Serina should have solved for x in the second equation because it has a coefficient of 1 .
D
Serina should have solved for y in the second equation because it has the largest coefficient.
4

Which statements about this system of equations are true? Choose three correct answers. 2 x minus 7 y is equal to negative 13 negative 2 x plus 11 y is equal to 1

A
The x -variable will be eliminated when adding the system of equations.
B
y is equal to negative 3
C
The y -variable will be eliminated when adding the system of equations.
D
The sum of the system of equations is 4 y is equal to negative 12 .
E
There are infinitely many solutions to the system of equations.
F
x is equal to 17
5

What is the solution to the system of equations? y is equal to 1 half x plus 6 and y is equal to negative 3 fourths x minus 4

A
open paren negative 8 comma negative 1 close paren
B
open paren negative 8 comma 2 close paren
C
open paren 8 comma 10 close paren
D
open paren 8 comma negative 10 close paren
7

Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that? 3 x minus 2 y is equal to 6 0 point 4 times open paren 20 y plus 15 close paren is equal to x

A
y is equal to negative 3 halves x plus 3 y is equal to 1 eighth x minus 3 fourths
B
y is equal to 3 halves x minus 3 y is equal to 1 fifth x minus 15 fourths
C
y is equal to 3 halves x minus 3 y is equal to 1 eighth x minus 3 fourths
D
y is equal to negative 3 halves x minus 3 y is equal to 1 fifth x minus 15 fourths
8

Which statements are true regarding the system of equations? Choose four correct answers. 4 x plus 5 y is equal to 15 28 x plus 35 y is equal to 105

A
The y -intercepts are different.
B
The system has an infinite number of solutions.
C
The system has one solution.
D
The system has no solution.
E
The y -intercepts are the same.
F
The lines coincide.
G
The lines are parallel.
H
The slopes are equal.
9

In the given system of equations, which variable would be easiest to solve for? x plus 4 y is equal to 14 3 x plus 2 y is equal to 12

A
The easiest to solve for is y in the second equation.
B
The easiest to solve for is x in the second equation.
C
The easiest to solve for is x in the first equation.
D
The easiest to solve for is y in the first equation.
10

Consider this system of equations. Which equation represents the first equation written in slope-intercept form? 5 x minus 2 y is equal to 10 y is equal to 1 fourth x plus 1

A
y is equal to negative 5 x minus 5
B
y is equal to 5 halves x plus 10
C
y is equal to negative 5 halves x plus 10
D
y is equal to 5 halves x minus 5
12

In one hour, a bakery sold 5 muffins and 9 bagels for total of $⁢25.50. The next hour, the bakery sold 3 muffins and 12 bagels for a total of $⁢28.50. Let m represent the price of one muffin and b represent the cost of one bagel. Draco wrote the following system of linear equations to solve for the cost of each item. 5 m plus 9 b is equal to 28 point 5 0 3 m plus 12 b is equal to 25 point 5 0 What is Draco’s error?

A
Draco should have written the second equation as 5 m plus 12 b is equal to 28 point 5 0 .
B
Draco should have written the first equation as 3 m plus 9 b is equal to 25 point 5 0 .
C
Draco should have written 9 b in the second equation and 12 b in the first equation.
D
Draco should have set the first equation equal to 25 point 5 0 and the second equation equal to 28 point 5 0 .
13

A system of equations is given. y is equal to negative 3 x plus 6 and y is equal to 6 minus 3 x Which of the following statements best describes the two lines?

A
They have different slopes and different y -intercepts, so they have no solution.
B
They have the same slope and the same y -intercept, so they have infinitely many solutions.
C
They have different slopes and different y -intercepts, so they have one solution.
D
They have the same slope and the same y -intercept, so they have no solution.
15

What is the slope of each line? Line cap A : y is equal to negative 4 x plus 5 Line cap b : y is equal to 3 x plus 1

A
The slope of line cap A is equal to 5 . The slope of line cap b is equal to 1 .
B
The slope of line cap A is equal to 1 . The slope of line cap b is equal to 5 .
C
The slope of line cap A is equal to negative 4 . The slope of line cap b is equal to 3 .
D
The slope of line cap A is equal to 4 . The slope of line cap b is equal to negative 3 .
16

Bryce took a quiz that consisted of true-or-false questions and multiple-choice questions. The true-or-false questions were worth 1 point each, and the multiple-choice questions were worth 2 points each. Bryce only knows that he answered 8 questions correctly and earned a total of 14 points. To determine the number of each type of question that he answered correctly, he wrote the system of linear equations x+y=8 and x+2⁢y=14. Which ordered pair is a solution to this system of linear equations, and what does the ordered pair represent?

A
open paren 8 comma 0 close paren ; Bryce answered 8 true-or-false questions correctly and 0 multiple-choice questions correctly.
B
open paren 2 comma 6 close paren ; Bryce answered 2 true-or-false questions correctly and 6 multiple-choice questions correctly.
C
open paren 6 comma 2 close paren ; Bryce answered 6 true-or-false questions correctly and 2 multiple-choice questions correctly.
D
open paren 0 comma 8 close paren ; Bryce answered 0 true-or-false questions correctly and 8 multiple-choice questions correctly.
17

Which explains why there is only one line?

A
Each has a slope of negative 3 and a y -intercept of negative 6 , so the system has no solution.
B
Each has a slope of negative 3 and a y -intercept of negative 6 , so the system has infinitely many solutions.
C
Each has a slope of negative 3 , but one has a y -intercept of 2 and the other has a y -intercept of negative 6 . So, the system has no solution.
D
Each has a slope of negative 3 , but one has a y -intercept of 2 and the other has a y -intercept of negative 6 . So, the system has infinitely many solutions.
18

Which equation, when graphed with the given equation, will form a system that has infinitely many solutions?

A
y is equal to negative 2 times open paren x minus 8 close paren
B
y is equal to negative open paren 2 x plus 8 close paren
C
y is equal to negative open paren negative 2 x plus 8 close paren
D
y is equal to negative 2 times open paren x minus 4 close paren

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