Systems of Linear Equations

Which system of two linear equations in two variables best represents the graph?

• y = 3x – 3

  y = -2x + 7

• y = 2x – 3

  y = -3x + 7

• y = 2x + 3

  y = -3x + 3.5

• y = 7x + 3.5

  y = x – 3

Two angles are supplementary angles. The first angle is six less than five times the second angle. Which of the following could be used to determine the measures of the angles?

• 180x = 5y – 6

  x – y = 180

• x + y = 90

  5y = x – 6

• x + y = 180

  y = 5x – 6

• x + y = 180

  5y = 6x – 5

Eight rectangles are stacked on top of

one another. The thickness of each rectangle is

either 1 inch or 2 inches. The height of the stack of

eight rectangles is 16 inches. Which system of

equations can be used to determine x, the number

of 1-inch thick rectangles in the stack, and y, the

number of 2 inch-thick rectangles in the stack?

• x + y = 16

  2x + y = 8

• x + y = 16

  x + 2y = 8

• x + y = 8

  x + 2y = 16

• x + y = 8

  2x + y = 16

The length of a rectangle is 7 inches

longer than its width. The perimeter of the

rectangle is 82 inches. Which of the following

systems of equations best describes the

dimensions of the rectangle?

• l + w = 7

  l + w = 82

• l – w = 7

  2l + 2w = 82

• l + w = 7

  2l + 2w = 82

• l – w = 7

  l + w = 7

A total of 1,650 boxes of cookies were sold last

week by a group of Girls Scouts. Each large box of

cookies cost $3.50, and each small box of cookies cost

$2.00. The Girl Scouts group earned $4,650. Which of

the following systems of equations could be used to

determine, l, the number of large boxes of cookies, and

s, the number of small boxes of cookies sold?

• 3.50l + 2.00s = 4,650

  l + s = 1,650

• 3.50l – 2.00s = 4,650

  l + s = 1,650

• 3.50l + 2.00s = 1,650

  l + s = 4,650

• 3.50s + 2.00l = 1,650

  l – s = 4,650

The Wildcats football team scored 12 times

each game, for a total of 72 points. Each

touchdown is worth seven points and each field

goal is worth three points. Which system of

equations could be used to find x, the number of

points earned from touchdowns, and y, the

number of points earned from field goals?

• x + y = 12

  7x + 3y = 72

• x + y = 72

  7x + 3y = 12

• 
  

  $x+y=12$
  

  
  $\frac{x}{7}+\frac{y}{3}=72$
  

• x + y = 72
  
  $\frac{x}{7}+\frac{y}{3}=12$
  

The graph represents a system of two linear equations in two variables. What is the system of linear equations that is shown on the graph?

• y = -3x + 4

  y = 3x – 2

• y = 3x + 4

  y = 3x + 2

• y = -3x + 1

  y = 3x – 2

• y = 4x – 3

  y = -2x + 3

Cameron needs to purchase red jelly beans

and white jelly beans for a party. The red jelly

beans cost $3.00 per pound, and the white jelly beans

cost $5.50 per pound. Cameron wants to buy a mixture

of both colors of jelly beans that weighs 7 pounds. He

has $20.25 to spend. Which system of two linear

equations could be used to determine the number of

pounds of red jelly beans, r, and white jelly beans, w,

Cameron could purchase?

• 3r + 5.5w = 20.25

  r + w = 7

• 5.5r + 3w = 20.25

  r + w = 7

• 3r + 5.5w = 7

  r + w = 20.25

• 8.5(r + w) = 20.25

  r + w = 7

A system of equations is graphed. What is the system of linear equations that is shown on the graph?

• 3x – 5y = 10

  x – 4y = 12

• 3x – 5y = 10

  x + 4y = 12

• 3x + 5y = 10

  x + 4y = 12

• 3x + 5y = 10

  x – 4y = 12

The two tables represent the values that correspond to a system of linear equations. What s the solution to this system of linear equations?

• (0, 2)

• (-2, 6)

• (-1, -5)

• (1, 0)