linear equations in two variables

Linear Equation in Two Variables

Prepared by:

Ms. Ma. Irene G. Gonzales

Lesson Objectives:

At the end of the period, students should be able to:

• illustrate linear equations in two variables;

• determine if an ordered pair is a solution of a given linear equation; and

• graph linear equations in two variables;

Linear Equation in Two Variables

An equation that can be written in the

standard form

Ax + By = C where A, B and C are real numbers but A

and B cannot both be zero.

Learning Objective: Students should be able to illustrate linear equations in two variables.

Determine whether or not each equation is a linear equation in two variables. If so, identify A, B and C.

5x = 10 + 3y is a

linear equation in

two variables

A = 5

B = -3

C = 10

5x = 10 + 3y

5x - 3y = 10 + 3y - 3y

5x – 3y = 10



y = 4x + 9 is a

linear equation in

two variables

A = 4

B = -1

C = -9

y = 4x + 9

y – 4x = 4x – 4x + 9

- 4x + y = 9

4x – y = -9



This is not a

linear equation

because the

exponent of x is

2.

3x2 – y = 9



This is not a linear

equation because a

variable appears in

the denominator of

a fraction.

203

yx



This is not a linear

equation because

the two variables

are part of the

same term.

15xy



x = 8 – 3y is a

linear equation in

two variables

A = 1

B = 3

C = 8

x = 8 – 3y

x + 3y = 8 – 3y + 3y

x + 3y = 8


Solutions of a Linear Equation in Two Variables

These are ordered pairs (x, y) that make the equation true.

Example 1:

Is the ordered pair (2, 2) a solution of x + 3y = 8?

How about (-1, 3)? (-2, -2)?

Learning Objective: Students should be able to determine if an ordered pair is a solution to a linear equation.

Determine if the given ordered pair is a solution of x + 4y = 7.

a. (3, 1)

b. (-1, 2)

c. (2, -1)


The question is…

Challenge Accepted!!!

Find three solutions of 4x + y = 12.

Solution: We find three ordered pairs that satisfy the given equation.


Learning Objective: Students should be able to graph linear equations in two variables.

linear equations in two variables

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