Solving Systems of Linear Equations: Linear Combinations
The system of equations below has no solution. Which equation could represent a linear combination of the system?
0=26
Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway. 30x + 30y = 45020x + 25y = 345 How much more can Paula shovel in 1 minute than Melinda? 3 square feet per minute 6 square feet per minute 9 square feet per minute 15 square feet per minute
3 square feet per minute
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? Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week. Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week. Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Which statement is true about the equations -3x + 4y = 12 and x - y = 1? The system of the equations has exactly one solution at (-8, 3). The system of the equations has exactly one solution at (-4, 3). The system of the equations has no solution; the two lines are parallel. The system of the equations has an infinite number of solutions represented by either equation.
The system of the equations has no solution; the two lines are parallel.
The system of equations shown is solved using the linear combination method What does 0 = 0 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines. There are no solutions to the system because the equations represent the same line. There are infinitely many solutions to the system because the equations represent parallel lines. There are infinitely many solutions to the system because the equations represent the same line.
There are infinitely many solutions to the system because the equations represent the same line
The system of equations is solved using the linear combination method. What does 0 = −12 mean regarding the solution to the system? There are no solutions to the system because the equations represent parallel lines. There are no solutions to the system because the equations represent the same line. There are infinitely many solutions to the system because the equations represent parallel lines. There are infinitely many solutions to the system because the equations represent the same line.
There are no solutions to the system because the equations represent parallel lines.
How many solutions are there to the system of equations? 4x-5y=5 -0.08x + 0.10y=0.10 no solutions one solution two solutions an infinite number of solutions
no solutions
