Lesson 8Shopping for Cats and DogsDevelop Understanding

Not all systems of equations have solutions. Determine which systems below have solutions and which ones don’t.

has a solution

no solution

has a solution

no solution

has a solution

no solution

has a solution

no solution

has a solution

no solution

has a solution

no solution

7.

What is it about a system of equations that would cause there to be no solution?

Set

8.

Mike and Gavin visited the amusement park with their science class on a school physics day. Their tickets were stamped each time they went on a ride. Mike and Gavin spent the entire afternoon going on their two favorite rides, the Roller Coaster and the Gravity Free-Fall. At the end of the day, their tickets were stamped as shown. Find the cost of each ride.

a.

Cost to ride the Roller Coaster?

b.

Cost to ride the Gravity Free-Fall?

9.

Mallory and Meg also attended the physics day with their school. Their favorite rides were Splash Peak and the Centrifugal Chamber. Here are their stamped tickets at the end of the day. Find the cost of each ride.

a.

Cost to ride Splash Peak?

b.

Cost to ride Centrifugal Chamber?

10.

Explain your process for determining the prices in problems 8 and 9. What’s the first thing that you look for or need to do?

Go

Write an inequality to describe the context. Graph each inequality. Then make a table that shows at least possible combinations that will work for each situation.

11.

Dion has enough money to buy up to eight yogurts. His favorite flavors are blueberry and strawberry.

Inequality:

12.

Shaniqua is buying a balloon bouquet. Her favorite colors are silver and purple. The silver balloons cost and the purple balloons cost . How many of each color of balloons can she put in her bouquet if she doesn’t spend more than ?

Inequality:

Graph the systems of inequalities to show the solutions for each system.