Solving Systems of Linear Equations: Substitution Answers

Vineet solved a system of equations by substitution. In his work, he substituted an expression for one of the variables and solved for the value of the other. This resulted in the equation 7 = 9. What can Vineet conclude?

y = 5.5xy = 10.5xy = 6.5x + 30y = 7.5x + 30

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y = [___]

Solve the system of equations by substitution.

y = 5.5xy = 10.5xy = 6.5x + 30y = 7.5x + 30

For the total cost to be the same for both companies, the volleyball team would need to purchase [___] T-shirts from each company for a total of $[___] for each company.

y = –2.5x – 15y = –2.5xy = 2.5x + 15y = 2.5x

2(8 – 3x) + 3x = 32x + 3(8 – 3x) = 32x + 3y = 8 – 3x

([___], [___])

Mr. Martin is giving a math test next period. The test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Write a system of equations that can be used to find how many problems of each point value are on the test.Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points.

How many problems of each point value are on the test?

For the total cost to be the same for both companies, the volleyball team would need to purchase [___] T-shirts from each company for a total of $[___] for each company.

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([___], [___])