Systems of Equations Review

A system of linear equations has no solutions. One of the equations of the system is shown: y = 2x - 1. Which equation could be the other equation of the system?

• y = -2x - 1

• y = 2x + 2

• A) no solution

• B) exactly one solution

• C) exactly two solutions

• D) infinitely many solutions

By inspection, how can you tell that a system has one solution?

• A) The slopes of the equations are the same so the lines will not intersect.

• B) The slopes of the equations are different so the lines will intersect at one point.

• C) The slopes of the equations are different so the lines will intersect twice.

• D) The slopes of the equations are the same so the lines will both be the same line.

How many solutions does the graph have?

• One solution

• No solution

• Three solutions

• Infinitely Many Solutions

How many solutions does the system of equations have?

• No solution

• One solution: (0, 5)

• One solution: (1, 4)

• Infinitely Many Solutions

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?

• 10 guests, $250

• 5 guests, $175

• 10 guests, $200

• 5 guests, $125

Naomi solves the following system of equations. What is the solution?

3y = 3x + 4

y = x + 3

• (0, 5)

• (9, 4)

• no solution

• infinitely many solutions

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

Solve the system of equations.

8t + 5h = 220

5t + h = 112

• t=20, h=12

• t=12, h=20

• t=8, h=5

• t=5, h=8

Uber charges a fee of $3.50, plus $1.75 per mile. Lyft charges a fee of $1.25, plus $2.00 per mile. At what distance would the ride cost the same?

• 2 miles

• 5 miles

• 9 miles

• 15 miles