SOLVING PROBLEMS
INVOLVING LINEAR
INEQUALITIES IN TWO
VARIABLES
Direction: Shade the side of the plane divider
where the solution of the inequality are found.
1. y < x + 3
2. y - x > - 5
3. x + y ≥ 1
4. 2x + y < 2
In solving problem involving linear
inequalities in two variables, you need to:
1. Read and analyze the problem carefully.
2. Identify the unknown.
3. Translate into mathematical phrase.
4. Sketch the graph of the inequality.
Sample Problem 1:
Elmo needs to score at least 45 points in a 25-item test in
Math to obtained a passing grade of 75%. Part I of the test
consists of 15 items and merits 2 points each while part II
consists of 10 items and merits 3 points each.
• a) Write and graph an inequality that represents the
number of each items in each part of the test.
• b) Give the possible combinations for the number of items
in each part to ensure a passing grade
Solution:
a)
Let x = number of items in part 1
Let y = number of items in part II
2x + 3y ≥ 45 the inequality Graph
b) The possible points (15, 5), ( 5, 10), (18, 6) are some of the solution
of the inequality:
Direction: Solve the following problem:
a) The length of a rectangle is 18 cm. What widths will give a
perimeter less than 150cm.
b) James has P250.00. He plans to buy his siblings a box of
pasalubong which consists of polvoron and pastillas. A pack of
polvoron costs P50.00 ans a pack of pastillas costs P40.00.
i. Make an inequality representing the number of packs of polvoron
and the number of packs of pastillas James can buy with P250.
ii. How many of each kind can he buy with his money?
HOMEWORK:
Direction: Solve the following problem:
Lola Kap has a hamburger and siomai stand. She
uses 25grams of ground pork for a hamburger
patty and 20 grams for each siomai. At least how
many siomai and patties can she make with 1/2
kg of ground pork?