Systems of Linear Equations Unit Test Review

The table can be used to determine the solution to the system of equations, 2y − x = 8, and y − 2x = −5. Which solution can be used to fill in both blanks in the table?

(6, 7)

A system of equations has infinitely many solutions. If 2y - 4x = 6 is one of the equations, which could be the other equation?

-y = -2x - 3

What is the x-value of the solution to the system of equations? 5x + 4y = 8 2x − 3y = 17

4

Martin has a combination of 33 quarters and dimes worth a total of $6. Which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, Martin has?

q + d = 33 0.25q + 0.1d = 6

Lukas graphed the system of equations shown. 2x + 3y = 2 y = 1/2x + 3 What is the solution to the system of equations?

(-2, 2)

What is the y-value of the solution to the system of equations? 3x + 5y = 1 7x + 4y = −13

2

Heather writes the equations below to represent two lines drawn on the coordinate plane. -6x + 18y = 0 4x - 12y = 20 After applying the linear combination method, Heather arrived at the equation 0 = 60. What conclusion can be drawn about the system of equations?

The equation has no solution; therefore, the system of equations has no solution.

A pilot flew a 400-mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind. What was the speed of the wind?

20 miles per hour

Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y = 10 + 3.5x Shop Dorian used: y = 6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental?

$24

Which is the best approximation for the solution of the system of equations? y = -2/5x + 1 y = 3x - 2

(0.88, 0.65)

What is the solution to the system of equations? y = 2x - 3.5 x - 2y = -14

(7, 10.5)

Which statements about the system are true? Check all that apply. y = 1/3x - 4 3y - x = -7

The system consists of parallel lines. Both lines have the same slope.

The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend. Which statement describes the amounts the team charged for wrapping gifts

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

A rectangular bird feeder costs $18.00. A cylindrical bird feeder costs $24.00. The expected cost to keep the rectangular bird feeder filled is $3.00 per week. The expected cost the keep the cylindrical bird feeder filled is $2.00 per week. The equation below models the break-even point. 18 + 3x = 24 + 2x What does x represent?

the number of weeks the bird feeders are filled

The solution to the system of equations shown is (2, 0). 3x − 2y = 6 x + 4y = 2 When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14 . Which system of equations will also have a solution of (2, 0)?

x + 4y = 2 7x = 14