Topic 4 - Systems of Linear Equations and Inequalities

What is the solution of the system of equations shown below?

y = −x + 3

y = 4x − 2

Which best describes the system of equations shown in the graph?

From the graph shown, what is an approximate solution of the system of equations?

y = −0.5x + 4

y = 1 + 2x

Caterer A charges $15 per person and $100 to set up tables. Caterer B charges $20 per person and $50 to set up tables. For how many guests will the cost of Caterer A be the same as the cost of Caterer B? What is that cost?

Number of guests: ​ (a)  

Cost: $ ​ (b)  

Use substitution to determine the solution of the system of equations.

y = −2x − 7

2y − x = 1

Naomi solves a system of equations using substitution. The system has infinitely many solutions. Which of the following could be the last step in Naomi's solution?

A store manager buys 8 T-Shirts and 5 hats for $220. The next day, the manager buys 5 T-shirts and 1 hat for $112. Select the system of equations that models the situation.

Use substitution to determine whether the system has no solution, infinitely many solutions, or one solution.

15x + 5y = 20

y = 8 − 3x

Solve the system using the elimination method. Write the solution as an ordered pair.

3x + 2y = 22

−x + 4y = 2

(​ (a)   , ​ (b)   )

Which of the following gives a valid reason for using the given solution method to solve the system of equations shown?

Equation I: 4x − 5y = 4

Equation II: 2x + 3y = 2