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

• (0, 3)

• (1, 2)

• (2, 1)

• (0, -2)

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

• no solution

• one solution

• infinitely many solutions

• two solutions

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

y = −0.5x + 4

y = 1 + 2x

• (1.25, 3.4)

• (2.25, 3.4)

• (3.4, 1.25)

• (3.4, 2.25)

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)  

• 10
• 250
• 0
• 100

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

y = −2x − 7

2y − x = 1

• (−1, 0)

• (21/2, -28)

• (-6, -5/2)

• (-3, -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?

• x = 0

• 3 = −3

• 2 = 2

• 5 = y

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.

• 8t + 5h = 220

  t + 5h = 112

• 13(t − h) = 220

  6(t − h) = 112

• 8t + 5h = 220

  5t + h = 112

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

15x + 5y = 20

y = 8 − 3x

• no solution

• infinitely many solutions

• one solution

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

3x + 2y = 22

−x + 4y = 2

(​ (a)   , ​ (b)   )

• 6
• 2
• 3
• -1

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

• Elimination; a coefficient in Equation I is an integer multiple of a coefficient in Equation II.

• Elimination; a coefficient in Equation II is an integer multiple of a coefficient in Equation I.

• Substitution; equation I can be solved for x in one step by dividing both

  sides by 4.

• Substitution; equation II can be solved for x in one step by subtracting 3y

  from both sides.