Question

priya’s pet store never has more than a combined total of 20 cats and dogs and never more than 8 cats. this is represented by the inequalities x + y ≤ 20 and x ≤ 8. solve the system of inequalities by graphing. a. graph a b. graph b c. graph c d. graph d

Explanation:

Step1: Analyze \( x \leq 8 \)

The inequality \( x \leq 8 \) (where \( x \) is cats) is a vertical line at \( x = 8 \), and the region includes all points to the left of or on this line.

Step2: Analyze \( x + y \leq 20 \)

Rewrite \( x + y \leq 20 \) as \( y \leq -x + 20 \). This is a line with slope -1, y - intercept 20, and x - intercept 20. The region is below or on this line.

Step3: Compare with graphs

• For \( x \leq 8 \), the vertical line should be at \( x = 8 \) (solid line, since \( \leq \)).
• Graph B has the vertical line at \( x = 8 \) (correct for \( x \leq 8 \)) and the line \( y=-x + 20 \) (correct for \( x + y \leq 20 \)), with the shaded region (implicitly) satisfying both inequalities. Other graphs: A has vertical line not at 8, C and D have incorrect vertical line positions or other issues.

Answer:

B. The graph labeled B (with vertical line at \( x = 8 \) and line \( y=-x + 20 \))