AnswersMathematics 8Linear Systems of Equations

Linear Systems of Equations — Test Answers

14 verified answers
1
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Which equation results from adding the equations in this system? negative 2 x plus y is equal to 8 5 x minus y is equal to negative 5

A
3 x is equal to 13
B
7 x is equal to 3
C
3 x is equal to 3
D
7 x is equal to 13
2
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Which statement is correct about the system of linear equations graphed here?

A
The system of equations has one solution because the lines will never intersect.
B
The system of equations has one solution because the lines will eventually intersect.
C
The system of equations does not have one solution because the lines will eventually intersect.
D
The system of equations does not have one solution because the lines will never intersect.
3

Consider the system of equations shown here. y is equal to negative 5 x plus 1 y is equal to negative 5 x plus 10 When graphed, the system consists of two lines that will never meet, no matter how far they are extended. Why are the lines parallel?

A
The linear equations have the same slope and y -intercept.
B
The linear equations have different slopes and y -intercepts.
C
The linear equations have different slopes but the same y -intercept.
D
The linear equations have the same slope but different y -intercepts.
4

Which system of equations has no solution?

A
y is equal to 4 x plus 5 and y is equal to 4 x minus 5
B
y is equal to 4 x plus 5 and y is equal to 8 x plus 10
C
y is equal to 4 x plus 5 and 2 y is equal to 8 x plus 10
D
y is equal to 4 x plus 5 and y is equal to 1 fourth x plus 5
5

What is the first step in solving the following system of equations? 3 x plus y is equal to 23 8 x plus 2 y is equal to 23

A
Substitute the value of x from one equation into the other equation.
B
Subtract the second equation from the first equation.
C
Substitute the value of y from one equation into the other equation.
D
Solve the first equation for y .
6

The monthly texting plan of All Star Cell is 11 dollars per month and 0 point 2 5 dollars per text. The monthly texting plan of Top Line Cell is 14 dollars per month and 0 point 1 5 dollars per text. A student wants to set up a system of equations to find the number of texts for which the total monthly cost of the two companies is the same. He uses the variables x and y He lets y represent the total monthly cost. What will x represent?

A
x is equal to total monthly cost
B
x is equal to cost of the total number of texts
C
x is equal to number of texts
D
x is equal to cost of each text
7

Dominique needs to solve the system of equations by graphing. Which statement is true about the system? 2 x minus 3 y is equal to 12 y is equal to negative 3 fifths x plus 2

A
The first equation is y is equal to 2 thirds x minus 4 when written in slope-intercept form.
B
The second equation is 3 x plus 5 y is equal to 10 when written in slope-intercept form.
C
Neither equation is in slope-intercept form.
D
Both equations are in slope-intercept form.
8

Company A sells hats for 11 dollars per hat plus a fixed 7 dollars shipping and handling fee. Company B sells hats for 8 dollars per hat plus a fixed 16 dollars shipping and handling fee. The marketing director of company A wants to set up a system of equations to find the number of hats for which the total cost of an order for the two companies is the same. He uses the variables x and y He lets y represent the total cost of an order. What will x represent?

A
x is equal to total cost of an order
B
x is equal to shipping costs for company A
C
x is equal to shipping costs for company B
D
x is equal to number of hats
9

Using the linear combination method, what is the solution to the system of linear equations 7 x minus 2 y is equal to negative 20 and 9 x plus 4 y is equal to negative 6 ?

A
open paren 2 comma negative 3 close paren
B
open paren negative 2 comma 3 close paren
C
open paren negative 3 comma 2 close paren
D
open paren 3 comma negative 2 close paren
10

Consider the system of linear equations 2 x plus 3 y is equal to 8 and 3 x plus y is equal to negative 2 Which statement is correct?

A
The point open paren 1 comma 2 close paren is a solution to the system of equations because it satisfies the equation 2 x plus 3 y is equal to 8 .
B
The point open paren 1 comma 2 close paren is not a solution to the system of equations because it satisfies neither equation.
C
The point open paren 1 comma 2 close paren is a solution to the system of equations because it satisfies both equations.
D
The point open paren 1 comma 2 close paren is not a solution to the system of equations because it does not satisfy the equation 3 x plus y is equal to negative 2 .
11

What is the slope of each line? Line cap A : y is equal to negative 5 x minus 2 Line cap b : y is equal to 2 x plus 3

A
The slope of line cap A is equal to negative 5 . The slope of line cap b is equal to 2 .
B
The slope of line cap A is equal to negative 2 . The slope of line cap b is equal to 3 .
C
The slope of line cap A is equal to 5 . The slope of line cap b is equal to negative 2 .
D
The slope of line cap A is equal to 3 . The slope of line cap b is equal to negative 2 .
12

What is the slope of each line? Line cap A : y is equal to 1 half x minus 4 Line cap b : y is equal to 2 x minus 3

A
The slope of line cap A is equal to negative 3 . The slope of line cap b is equal to negative 4 .
B
The slope of line cap A is equal to 1 half . The slope of line cap b is equal to 2 .
C
The slope of line cap A is equal to negative 4 . The slope of line cap b is equal to negative 3 .
D
The slope of line cap A is equal to negative 1 half . The slope of line cap b is equal to negative 2 .
13

The equations in the given system are equivalent. y is equal to 2 times open paren x plus 4 close paren y is equal to 2 x plus 8 How many solutions does the system have?

A
two solutions
B
no solution
C
an infinite number of solutions
D
one unique solution
14

Which graph represents a system of equations with one solution?

A
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. A line passes through (negative 2 comma negative 2) and (0 comma 4). A line passes through (0 comma 2) and (1 comma 5).
B
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. A line passes through (0 comma 2) and (1 comma 5). A line passes through (0 comma negative 2) and (1 comma 2).
C
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. A line passes through (0 comma 2) and (0 point 5 comma 3). A line passes through (0 comma 4) and (0 point 5 comma 3).
D
Image with description On a coordinate plane, the x-axis ranges from negative 5 to 5 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1. A line passes through (0 comma 2) and (1 comma 5).

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