The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

1. Linear Equation in Two Variables
Prepared by:
Ms. Ma. Irene G. Gonzales

2. 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;

3. 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.

4. 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
Learning Objective: Students should be able to illustrate linear equations in two variables.

5. Determine whether or not each equation is a linear
equation in two variables. If so, identify A, B and C.
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
Learning Objective: Students should be able to illustrate linear equations in two variables.

6. Determine whether or not each equation is a linear
equation in two variables. If so, identify A, B and C.
This is not a
linear equation
because the
exponent of x is
2.
3x2 – y = 9
Learning Objective: Students should be able to illustrate linear equations in two variables.

7. Determine whether or not each equation is a linear
equation in two variables. If so, identify A, B and C.
This is not a linear
equation because a
variable appears in
the denominator of
a fraction.
20
3
 y
x
Learning Objective: Students should be able to illustrate linear equations in two variables.

8. Determine whether or not each equation is a linear
equation in two variables. If so, identify A, B and C.
This is not a linear
equation because
the two variables
are part of the
same term.
15xy
Learning Objective: Students should be able to illustrate linear equations in two variables.

9. Determine whether or not each equation is a linear
equation in two variables. If so, identify A, B and C.
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
Learning Objective: Students should be able to illustrate linear equations in two variables.

10. 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.

11. Determine if the given ordered pair is a
solution of x + 4y = 7.
a. (3, 1)
b. (-1, 2)
c. (2, -1)
Learning Objective: Students should be able to determine if an ordered pair is a solution to a
linear equation.

12. The question is…

13. 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 determine if an ordered pair is a solution to a
linear equation.

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