Modeling Linear Systems

Anna is an avid reader. Her generous grandparents gave her money for her birthday, and she decided to spend at most $150.00 on books. Reading Spot is running a special: all paperback books are $8.00 and hardback books are $12.00. Anna wants to purchase at least 12 books. Let x represent the number of hardback books and y represent the number of paperback books. Which of the following systems of inequalities correctly represents the given constraints.

• {12x+8y≤150

  x+y≥12

  where x and y are whole numbers

• {12x+8y>150

  x+y≥12

  where x and y are whole numbers

• {12x+8y>150

  x+y<12

  where x and y are whole numbers

Select the system that has the same solution as

{-2x+2y=-5

5x-6y=8

• {3x-4y=3

  -5x-6y=8

• {6x+6y=15

  5x-6y=8

• {3x-4y=3

  15x-18y=24

• {-2x+2y=-5

  10x-12y=8

Ten bagels and four muffins cost 13$. Five Bagels and eight muffins cost 14$. How much does a bagel cost?

Ten bagels and four muffins cost 13$. Five Bagels and eight muffins cost 14$. How much does a Muffin cost?

Select the correct equation.

The equation y=6.75x models the cost, in dollars, to purchase x pounds of steak at grocery store 1. Which equation models the cost of x pounds of steak at grocery store 2?

Fabiola is reviewing for the Algebra 1 End-of-Course exam. She made this graph representing a system of inequalities. Select the ordered pairs below that represent solutions to the system of inequalities.

• (-6,3)

• (-6,6)

• (-5,0)

• (-4,2)

• (-4,0)

Latisha wants to buy pumpkin and autumn squash for a fall display. She has a budget of no more than $117 but wants to buy more than 10 vegetables for the decorations. The pumpkins are $5.50 each and the autumn squash are $3.50 each.

Write a system of inequalities to represent the situation.

• 5.50x+y>117

  3.50y<110

• 5.50x + 3.50y ≤ 117

  x+y>10

• x+y>10

  5.50x + 3.50y ≤ 117

• 1.25x+10<117

  x+y>8

Select the point that is included in the solution set of the system of inequalities.

y≥x-3

y≥-x-1

• (0,-10)

• (2,2)

• (-4,-2)

• (-3,-4)

What is the Y-coordinate in the solution for the system of linear equations below?

{5x-2y=4

3x-4y=-6

• y=2

• y=-2

• y=3

• y=-3