Solving Systems of Linear Equations: Substitution: Assignment

Solve the system of equations by substitution. 3/8x + 1/3y = 17/24 x + 7y = 8

(1, 1)

Use the system of equations to answer the questions. 2x + 3y = 3 y = 8 - 3x The value of y from the second equation is substituted back into the first equation. What is the resulting equation? What is the value of x? What is the value of y?

1. 2x+3(8-3x)=3 2. 3 3. -1

The tables represent two linear functions. The equation represented by the first table is given below. y = 5.75x + 34.5 What linear equation is represented by the second table? What is the solution to the system of equations?

1. y=-2.5-15 2. (-6, 0)

The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The graph represents the two companies' prices. What is the linear equation that represents each T-shirt company? Shirt Box: Just Tees:

1. y=7.5x=30 2. y=10.5x

The value of x in this system of equations is 1. 3x + y = 9 y = -4x + 10 Substitute the value of y in the first equation: Combine like terms: Apply the subtraction property of equality: Apply the division property of equality: 1. 3x + (-4x + 10) = 9 2. -x + 10 = 9 3. -x = -1 4. x = 1 What is the value of y? y=

6

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.

A. x + y = 29, 5x + 2y = 100

Mr. Martin's math test, which is worth 100 points, has 29 problems. Each problem is worth either 5 points or 2 points. Let x be the number of questions worth 5 points and let y be the number of questions worth 2 points. x + y = 29, 5x + 2y = 100 How many problems of each point value are on the test?

B. 14 problems worth 5 points and 15 problems worth 2 points

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?

B. The system of equations does not have a solution.

The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The two companies, Shirt Box and Just Tees, are represented by this system of equations where x is the number of T-shirts and y is the total cost of the T-shirts. y = 10.5x y = 7.5x + 30 How many T-shirts would the volleyball team need to purchase from each company for the total cost to be equal? 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.

Blank 1: 10 Blank 2: 105

When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation. Nicole found x = y - 10 for the same equation and substituted y - 10 for x in the other equation. Who is correct? Explain.

Sample Answer: Both Jared and Nicole are correct. You can solve for either variable and use the equivalent expression to create a one-variable equation. Then you can solve. Jared would have created a one-variable equation that can be used to solve for x, whereas Nicole would have created a one-variable equation that can be used to solve for y.