Systems of Linear Equations EOC Review

A customer paid a total of $6.00 for 68 copies at a print shop. Some of the copies were black-and-white copies, and the rest were color copies. - Each black-and-white copy cost $0.08. - Each color copy cost $0.15. Which system of equations can be used to find b, the number of black-and-white copies, and c, the number of color copies that the customer paid for at the print shop?

• b + c = 6.00 0.08b + 0.15c = 68

• b + c = 68 0.15b + 0.08c = 6.00

• b + c = 6.00 0.15b + 0.08c = 68

• b + c = 68 0.08b + 0.15c = 6.00

What is the value of x in the solution to this system of equations? 3x - 5y = 22 y = -5x + 32

• -6.5

• 0.5

• 6.5

• -0.5

A drummer and a guitarist each wrote songs for their band. The guitarist wrote 8 fewer than twice the number of songs that the drummer wrote. They wrote a total of 46 songs. Which system of equations models this situation if the drummer wrote d songs and the guitarist wrote g songs?

• g = 2d - 8 g + d = 46

• g = 8 - 2d g = 46 - d

• d = 2g - 8 d = 46 - g

• d = 8 - 2g d + g = 46

What is the value of y in the solution to this system of equations? 6y + x = -59 x = -2y + 9

• 8.5

• -17

• 43

• -12.5

The graphs of lines k_1 and k_2 are shown on the grid. Which system of equations is best represented by this graph?

• 3x - y = 2 and 4x + 9y = 36

• 3x - y = 6 and 4x + 9y = 4

• x - 3y = -18 and 9x + 4y = 9

• x + y = 10 and 9x + 4y = 13

A system of linear equations is represented by line h and line j. A table representing some points on line h and the graph of line j are shown. Which system of equations is best represented by lines h and j?

• y = \frac{4}{3}x - 5 and y = \frac{4}{5}x + 1

• y = \frac{3}{4}x - 5 and y = \frac{5}{4}x + 1

• y = -\frac{4}{3}x - 5 and y = -\frac{4}{5}x + 1

• y = -\frac{3}{4}x - 5 and y = -\frac{5}{4}x + 1

The following represents the first of two equations in a system of linear equations. The graph of the second equation in the system passes through the point (-4, 0) and (12, 8). What is the solution to the system?

• The only solution to the system is (-12, -4).

• The only solution to the system is (4, 4).

• The system has no solution.

• The system has an infinite number of solutions.

What is the solution to the following system of equations? x + 2y = 8 y = -1/2x + 4

• The ordered pair (0, -9/2) is the solution.

• The ordered pair (6, 0) is the solution.

• There are an infinite number of solutions.

• There is no solution.

What is the solution(s), if any, to the system of linear equations below? 3x + 2y = 10 y = -3/2x - 4

• (-2, 3)

• (3, -2)

• no solution

• infinitely many solutions