Solving Systems of Linear Equations: Substitution Answers

What is the solution to the system of equations?y = 1.5x – 4y = –x

Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.

What is the solution to the system of equations?y = x + 3x = –2

y=4x – 10y=2

The tables represent two linear functions in a system.What is the solution to this system?

y=–3x + 6y=9

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.x – y = 73x – 2y = 8Step 1: x = y + 7Step 2: 3(y + 7) – 2y = 8Step 3: 3y + 7 – 2y = 8Step 4: y + 7 = 8Step 5: y = 1

y=–5x + 30x=10

The soccer team is planning to sell health bars for a fundraiser. The prices of purchasing health bars from two different companies are represented by the system of equations shown, where x is the number of bars purchased and y is the total cost in dollars.Company A: y=0.75xCompany B: y=10+0.50x

Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?