Linear Equations and Inequalities in Two Variables

Janel bought three apples and two oranges. The total amount she paid was at most Php 123. If x represents the number of apples and y the number of oranges, which of the following mathematical statements represents the given situation?

• 3x + 2y ≥ 123

• 3x + 2y ≤ 123

• 3x + 2y > 123

• 3x + 2y < 12

How many solutions does a linear inequality in two variables have?

• 0

• 1

• 2

• infinite

Adeth has some Php 10 and Php 5 coins. The total amount of these coins is at most Php 750. Suppose there are 50 Php 5-coins. Which of the following is true about the number of Php 10-coins?

I. The number of Php 10-coins is less than the number of Php 5-coins.

II. The number of Php 10-coins is more than the number of Php 5-coins.

III. The number of Php 10-coins is equal to the number of Php 5-coins

• I and II

• I and III

• II and III

• I, II, and III

Which of the following ordered pairs is a solution of the inequality 2x + 6y ≤ 10?

• (3, 1)

• (2, 2)

• (1, 2)

• (1, 0)

What is the graph of linear inequalities in two variables?

• Straight line

• Half-plane

• Parabola

• Half of a parabola

The difference between the scores of Connie and Minnie in the test is not more than six points. Suppose Connie’s score is 32 points, what could be the score of Minnie?

• 26 to 38

• 38 and above

• 26 and below

• Between 26 and 38

Which of the following forms of linear inequality is not included

• Ax + By < C

• Ax + By ≤ C

• Ax + By > C

• Ax + By ≠ C

In the inequality c – 4d ≤ 10, what could be the possible value of d if c = 8?

• d ≤ -1/2

• d ≥ -1/ 2

• d ≤ 1/2

• d ≥ 1/2

Mary and Rose ought to buy some chocolates and candies. Mary paid Php 198 for six bars of chocolates and 12 pieces of candies. Rose bought the same kinds of chocolates and candies but only paid less than Php 100. Suppose each piece of candy costs Php 4, how many bars of chocolates and pieces of candies could Rose have bought?

• 4 bars of chocolates and 2 pieces of candies

• 3 bars of chocolates and 8 pieces of candies

• 3 bars of chocolates and 6 pieces of candies

• 4 bars of chocolates and 4 pieces of candies

Which of the following is a linear inequality in two variables?

• 4a – 3b = 5

• 3x ≤ 16

• 7c + 4 < 12

• 11 + 2t ≥ 3s11