Systems Review

What is the solution to the following system?

3x + y = 14

-x + y = 2

• (5,3)

• (-3,5)

• (3,5)

• (5,-3)

The perimeter of a rectangle is 24 meters. The width is nine meters less than twice the length. Which system of equations could be used to find the width, w, and the length, l, of the rectangle?

Hint: P=2l + 2w

• w= 2l - 9

  l + w = 24

• w = 9- 2l

  2l + 2w = 24

• w = 2l - 9

  2l + 2w = 24

• w = 9l - 2

  l + w = 24

A group of 19 people (adults and children) went to a concert for 5 hours. Each adult paid $9 and each child paid $4. Altogether the group paid $111. Find the system of equations that could be used to find the number of adults, a, and the number of children, c.

• a + c = 111

  9a + 4c = 19

• a + c = 19

  9a + 4c = 111

• 5a + 5c = 19

  9a + 4c = 111

• a + c = 19

  5(9a + 4c) = 111

What are the coordinates of the point of intersection of the two lines below?

2x + 3y = 12

x + 4y = 16

• (-4,0)

• (0,4)

• (4,0)

• (0,-4)

The graph of y = 2x - 1 is given below (on your paper). Graph y = x + 2 on the graph and identify the solution to the system of equations.

• (1,1)

• (3,5)

• (2,3)

• (-1,-3)

Mr. Leblanc saves nickels and dimes. If he has 28 coins worth $2.60, which system of equations could be used to find n, the number of nickels, and d, the number of dimes that Mr. Leblanc has?

• n + d = 28

  5n + 10d = 260

• n + d = 2.60

  .05n + .10d = 28

• n + d = 28

  .10n + .05d = 2.60

• n + d = 28

  .05n + .10d = 2.60

Which of the following points are solutions to the system below?

3x + 2y < 28

x - 2y <= 0

• (1,3)

• (3,-4)

• (0,-5)

• (1,-1)

Two cans of paint and one roller cost $58. Three cans of the same paint and two rollers cost $92. What is the price for one roller?

Select the inequality that best represents the graph (on your paper).

• x < -2

• y < -2

• x > -2

• y > -2

Which ordered pair is in the solution set of the following system of inequalities?

3x + 4y > 12

y > 2x - 1

• (3,-5)

• (6,0)

• (-8,-1)

• (-2,6)