Solving Systems of Linear Equations: Linear Combinations: Quiz

Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below. 5x+2y=8 -4(1.25x+0.5y=2)/5x+2y=8 -5x-2y=-8/0=0

D. infinitely many solutions

The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 1/4(4x - 8y = 12) → x - 2y = 3 2x = 18 What is the solution of the system of equations?

D. (9, 3)

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. Which statement describes when the plans are based on the same number of aerobic exercise sessions?

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

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 = 28 Second equation: 3x - 9y = 30

D. The first equation should be multiplied by 9 and the second equation by −4.

Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 -3x + 5y = 10

A. (0, 2)

The system of equations is solved using the linear combination method. 1/2x+4y=8 → -2(1/2x+4y=8) → -x-8y=-16 3x+24y=12 → 1/3(3x+24y=12) → x+8y=12 0=-12 What does 0=-12 mean regarding the solution to the system?

A. There are no solutions to the system because the equations represent parallel lines.

The system of equations below has no solution. 2/3x+5/2y=15 4x+15y=12 Which equation could represent a linear combination of the system?

B. 0=26

Which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98

C. The lines intersect at (1.6,1.4).

Which statement is true about the equations -3x + 4y = 12 and 1/4x - 1/3y = 1?

C. The system of the equations has no solution; the two lines are parallel.

How many solutions are there to the system of equations? 4x-5y=5 -0.08x+0.10y=0.10

A. no solutions