Illustrating Linear Equations in Two Variables

If 𝐴, 𝐵, and 𝐶 are real numbers and if 𝐴 and 𝐵 are both not equal to 0 then 𝐴𝑥 + 𝐵𝑦 = 𝐶 is called a __________.

• linear equation in one variable

• linear equation in two variables

• system of linear equations

• system of linear inequalities

Which of the following is the standard form of a linear equation in two variables?

• 𝑦 = 𝑚𝑥 + b

• 𝑦 = 𝑚𝑥 – b

• 𝐴𝑥 + 𝐵𝑦 = C

• 𝐴𝑥 − 𝐵𝑦 = C

What is 𝐶 in the equation 𝐴𝑥 + 𝐵𝑦 = 𝐶?

• coefficient

• constant

• slope

• variable

If written in standard form, what is the value of 𝐵 in the equation 4𝑦 − 5 = 𝑥?

• −5

• −4

• 0

• 1

On his notes on linear equation in two variables, Joshua found an equation 2𝑥 + 3𝑦 = 10. If you were Joshua, how would you describe the equation according to its form?

• It has constant

• It has variables

• It is in standard form

• It is in slope-intercept form

Which statement below DOES NOT satisfy the definition of linear equation in two variables?

• It has no variable inside a radical sign.

• The equation has variable in the denominator.

• The standard form of the equation is 𝐴𝑥 + 𝐵𝑦 = 𝐶.

• The highest exponent of the variable in each term is 1.

In the equation 𝐴𝑥 + 𝐵𝑦 = 5, what happens when 𝐴 and 𝐵 are both zero?

• The equation remains true

• The equation is not defined

• The graph of the equation is vertical

• The graph of the equation is horizontal

What value of 𝑥 would make 𝑦 = 1 in the equation 3𝑥 + 𝑦 = 4?

• -1

• 0

• 1

• 2

The following are situations which can be modelled by linear equations in two variables EXCEPT ONE. Which is it?

• calculating the perimeter of a rectangle

• calculating the wage of an employee based on hourly rate

• finding the total number of bacteria that doubles every hour

• cost of hiring a car when a deposit is paid and there is a daily charge

During weekends, Marco cleans the basketball court in his barangay and gets paid Php35 per hour and a cash allowance. If you want to compute Mario’s total pay given the number of hours 𝑥 and a cash allowance 𝑦, which of the following model is appropriate?

• 𝑥 + 𝑦 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎y

• 𝑥 + 35𝑦 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎y

• 35𝑥 + 𝑦 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎y

• 35𝑥 + 35𝑦 = 𝑡𝑜𝑡𝑎𝑙 𝑝𝑎y