Multiplying One Equation to Solve Systems Answers

Which value of k would cause the system of linear equations and to have an infinite number of solutions?

Which of these systems of linear equations has no solution?

To solve the system of linear equations and by using the linear combination method, Laura correctly multiplied the first equation by –2 to get and then correctly added the equations and to get 0 = 4. How many solutions are there to the system of equations?

Denise bought 116 ounces of beans for a bean dip. She bought both 15-ounce cans and 28-ounce cans, and the total number of cans she bought was 6. Which of these systems of equations can be used to determine the number of 15-ounce cans and the number of 28-ounce cans that she bought? Assume x represents the number of 15-ounce cans and y represents the number of 28-ounce cans.

To solve the system of linear equations and by using the linear combination method, Henry decided that he should first multiply the first equation by –3 and then add the two equations together to eliminate the x-terms. When he did so, he also eliminated the y-terms and got the equation 0 = 0, so he thought that the system of equations must have an infinite number of solutions. To check his answer, he graphed the equations and with his graphing calculator, but he could only see one line. Why is this?

Rob is a high school student taking both algebra and geometry. Last night he had 27 homework problems combined from the two classes, and he took a total of 90 minutes to do them. If each algebra problem took him 2 minutes and each geometry problem took him 5 minutes, how many algebra problems did he have for homework?

Which of these statements is correct?

A company has a $150 budget to provide lunch for its 20 employees. The options are to provide either roast beef sandwiches, which cost $5 apiece, or tuna sandwiches, which also cost $5 apiece. The company also wants to use the entire budget. Suppose r represents the number of roast beef sandwiches it provides and t represents the number of tuna sandwiches. Which statement is correct?

Michiko claims that to solve the system of linear equations and , instead of multiplying the second equation by –2 and then adding the equations, she could multiply the second equation by 2 and then subtract the second equation from the first equation. Which statement is correct?

Which of these systems of linear equations has an infinite number of solutions?