Q1M8 SOLVING PROBLEMS INVOLVING SYSTEMS OF LINEAR EQUATIONS IN TWO VARIABLES

The following systems of equations show coincident lines with infinitely many solutions. Which of these has some solutions such as (−1, 13), (0, 10), (1, 7) and (2, 4)?

• a.

• b.

• c.

• d.

Which of the following is a solution to the the system 3x+2y=7 and x-5y=8?

• (1, 3)

• (3, 1)

• (-1, 3)

• (3, -1)

What is the solution of 𝑥 – 𝑦 = 4 and 𝑥 = 2𝑦 if substitution is applied?

• (8, 4)

• (4, 8)

• (-8, 4)

• (-4, 8)

What is the solution or solution set of the system of linear equations given by 2𝑥 – 6𝑦 = 4 and 𝑥 = 3𝑦 + 4 when solved using substitution?

• (1, 0)

• (2, 0)

• no solution

• infinitely many solutions

Which of the following ordered pairs does not satisfy both 2𝑥 – 4𝑦 – 8 = 0 and 𝑥 = 2𝑦 + 4 if substitution is applied?

• (0, -2)

• (4, 0)

• (-2, 3)

• (2, -1)

What expressions should be multiplied to the system of linear equations 2𝑥 + 4𝑦 = 8 and 𝑥 – 𝑦 = 4 to eliminate first a variable y?

• 2

• 4

• 6

• 8

What is the solution to the systems 𝑥 + 2𝑦 = 2 and 𝑥 – 2𝑦 = 2 when solved using elimination method?

• (0, 2)

• (0, -2)

• (2, 0)

• (-2, 0)

Which of the following is a solution to the system of linear equations 𝑥 – 𝑦 = 4 and 2𝑥 + 2𝑦 = 8 when solved using elimination method?

• (0, 4)

• (4, 0)

• (0, -4)

• -4, 0)

Elena went to a fast food restaurant. Four cheeseburgers and 2 large cokes cost a total of Php 118.00. Two large cokes cost Php 3.00 more than one cheeseburger. Let it be x for the cost of cheeseburger and y for the cost of a large coke. What mathematical equations can we get from the statement?

• a.

• b.

• c.

• d.

Elena went to a fast food restaurant. Four cheeseburgers and 2 large cokes cost a total of Php 118.00. Two large cokes cost Php 3.00 more than one cheeseburger. Let it be x for the cost of cheeseburger and y for the cost of a large coke. What is the cost of a cheeseburger?

• Php 13.00

• Php 23.00

• Php 33.00

• Php 43.00