﻿ Graphing Inequalities in Two Variables Worksheet - Page 2 | Problems & Solutions

# Graphing Inequalities in Two Variables Worksheet - Page 2

Graphing Inequalities in Two Variables Worksheet
• Page 2
11.
Determine whether the ordered pair (5, 20) is a solution of the inequality $y$ < $x$2 + $x$ - 10.
 a. Yes b. No

#### Solution:

y < x2 + x - 10
[Write original inequality.]

20 < 52 + 5 - 10
[Substitute 5 for x and 20 for y.]

20 < 25 + 5 - 10
[Evaluate the exponent.]

20 < 20
[Simplify.]

20 is not less than 20.

The ordered pair (5, 20) is not a solution to the inequality y < x2 + x - 10.

12.
David can afford to buy 15 mangoes and 20 oranges. He wants at least 10 mangoes and at least 10 oranges. If $x$ represent the number of mangoes ,$y$ represent the number of oranges that David buy , then which of the following systems of inequalities models this situation?
 a. $x$ ≥ 15, $y$ ≥20, $x$ ≥ 10, $y$ ≥ 10 b. $x$ ≤ 15, $y$ ≥20, $x$ ≥ 10, $y$ ≥ 10 c. $x$ ≤ 15, $y$ ≤20, $x$ ≥ 10, $y$ ≤ 10 d. $x$ ≤ 15, $y$ ≤ 20, $x$ ≥ 10, $y$ ≥ 10

#### Solution:

x represents the number of mangoes bought and y represents the number of oranges that David buy

The maximum number of mangoes that can be bought is 15. So x ≤ 15.

The maximum number of oranges that can be bought is 20. So y ≤ 20.

The minimum number of mangoes to be bought is 10. So x ≥10.

The minimum number of oranges to be bought is 10. So y ≥ 10.

So, the system of inequalities that models the given situation is:
x ≤ 15, y ≤ 20, x ≥ 10, y ≥ 10.

13.
If the cost of a tape is $10 and the cost of a CD is$12, then write the objective function for the cost of $x$ tapes and $y$ CDs .
 a. C = 12$x$ + 10$y$ b. C = 22 + $x$ + $y$ c. C = 10$x$ + 12$y$ d. C = 120$\mathrm{xy}$

#### Solution:

The cost of each tape is $10 and the cost of each CD is$12.

The cost C of x tapes and y CDs is C = 10x + 12y, which is the objective function for the cost.