Write a system of inequalities to model the situation, then graph.

Question

Renee's pet store has no more than a combined total of 20 cats and dogs. She has no more than 8 cats at one time.

Answer 1

Let number of cats = x

Let number of dogs = y

 

Use these variables to set up inequalities.

 

x + y ≤ 20             ineq1

 

x ≤ 8                     ineq2

 

 

From ineq1,

 

y ≤ -x + 20

 

 

Graph the bolded inequalities. 

 

Inequality one is the line      y=-x+20        shaded below the line.

Inequality two is the vertical line at    x=2    shaded to the left of the line.

 

The solution set is the overlapping shaded region.