AnswersFL-1200310-Algebra 1Solving Systems of Linear Equations: Linear Combinations

Solving Systems of Linear Equations: Linear Combinations Answers

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The linear combination method is applied to a system of equations as shown.4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18

Question illustration
A
(1,2)
B
(3,9)
C
(5,5)
D
(9,3)
2
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The system of equations is solved using the linear combination method.What does 0 = −12 mean regarding the solution to the system?

Question illustration
A
There are no solutions to the system because the equations represent parallel lines.
B
There are no solutions to the system because the equations represent the same line.
C
There are infinitely many solutions to the system because the equations represent parallel lines.
D
There are infinitely many solutions to the system because the equations represent the same line.
3

At what value of x do the graphs of the equations below intersect?2x − y = 65x + 10y = −10

A
Option
Option A
B
−2
C
2
D
Option
Option D
4

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First Equation: 5x − 4y = 28Second equation: 3x - 9y = 30

A
The first equation should be multiplied by 3 and the second equation by 5.
B
The first equation should be multiplied by 3 and the second equation by −5.
C
The first equation should be multiplied by 9 and the second equation by 4.
D
The first equation should be multiplied by 9 and the second equation by −4.
5

Which statement describes the graph of the system of equations below?1.5x + 0.2y = 2.681.6x + 0.3y = 2.98

A
The lines are parallel.
B
The lines overlap at all points.
C
The lines intersect at (1.6,1.4).
D
The lines intersect at (3.1,0.5).
6

Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61300x + 30y = 75.90

A
The cost of natural gas is $0.17 per unit.
B
The cost of natural gas is $0.20 per unit.
C
The cost of natural gas is $0.72 per unit.
D
The cost of natural gas is $0.83 per unit.
7

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.

A
Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
B
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
C
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
D
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
8

The system of equations shown is solved using the linear combination methodWhat does 0 = 0 mean regarding the solution to the system?

Question illustration
A
There are no solutions to the system because the equations represent parallel lines.
B
There are no solutions to the system because the equations represent the same line.
C
There are infinitely many solutions to the system because the equations represent parallel lines.
D
There are infinitely many solutions to the system because the equations represent the same line.
9

The system of equations below has no solution.

Question illustration
A
Four-thirds x = 42
Option A
B
Option
Option B
C
Fifteen-halves y = 33
Option C
D
0 = 0
Option D
10

To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: Second equation:

Question illustration
A
The first equation should be multiplied by 3 and the second equation by -5.
B
The first equation should be multiplied by 3 and the second equation by 5.
C
The first equation should be multiplied by 7 and the second equation by -6.
D
The first equation should be multiplied by 7 and the second equation by 6.

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