1. The document presents examples of solving addition and subtraction problems with positive and negative numbers. It also gives examples of finding two numbers whose sum and difference satisfy given values. 2. It defines a system of linear equations as two equations in two variables of the form Ax + By = C and Dx + Ey = F. It explains that an ordered pair (x,y) is a solution if it satisfies both equations. 3. Examples are given of determining if an ordered pair is a solution to a given system of linear equations by substituting the values into each equation and checking if both equations are satisfied. An activity asks students to identify if ordered pairs are solutions to several systems.

1. Presented by: Mr. Joseph C. Nilo

2. Simplify the following
1.(-2) + (-3)
2.(-6) + 5
3.(3) + (-3)
4. (-2) – (-3)
5. (-6) – (5)
6. (3) – (-3)

3. Problem of the day!!!
 Find two numbers whose sum and
difference are the following:
Sum Difference Answer
5 1 3 and 2
5 3 4 and 1
-2 0 -1 and -1
-2 -12 -7 and 5

4. System of Linear Equation & their Solution
 A pair of equation of the form
Ax + By = C
Dx + Ey = F
Where A, B, D, and E are not equal to zero is
called a system of linear equation in two
variables
 An ordered pair (x , y) is a solution set of the
system of linear equations which satisfies
both of the equation

5. Illustrative Example
 Determine whether (-1, 2) is a solution
of 3x + y = - 1 and 2x + 4y = 8
Solution:
* 3x + y = - 1
3(-1)+(2) = - 1
- 3 + 2 = - 1
- 1 = - 1
* 2x + 4y = 8
2(-1) + 4(2) = 8
- 2 + 8 = 8
6 ¹ 8

6.  Although (1, 2) makes the
first sentence / equation
true it does not satisfy the
second and therefore it
can’t be accepted as a
solutions of the system

7.  Determine whether (2, -3) is a solution
of 2x + 2y = -2 and 3x + 2y = 0
* 2x + 2y = - 2
2(2)+2(-3) = - 2
4 - 6 = - 2
- 2 = - 2
* 3x + 2y = 0
3(2) + 2(-3) = 0
6 - 6 = 0
0 = 0
 The pair (2, -3) makes both equation
true so it is a solution of the system

8. Activity: Cooperative Learning
 Write (Ö) whether the ordered pair beside
each system is a solution and (X) if not a
solution of the system.
• (4, 8) ; x + 2y = 20
3x – 4y = 12
• (5, - 4) ; 4x + 3y = 8
x + y = 1
• (0, 2) ; x + y = 2
x = 0
X
Ö
Ö

9. Communicating
Skills
When do we say that a
given pair of real
numbers is a solution
of the system?

10. Test Proper
 Write (Ö) whether the ordered pair
beside each system is a solution and
(X) if not a solution of the system
• (5, -1) ; 2y + x = 5
3y + 4x = - 19
• (½ , 3) ; 4x + 8y = 26
6x - 2y = - 3
X
Ö

11. Assignment
A. Answer the following
 List 5 ordered pairs which satisfy the
equation x + y = 6
 List 5 ordered pairs which satisfy the
equation x – y = 8
 What is ordered pair that satisfies both
equations in number 1 and 2
B. Bring the following: Each group
 10 pcs. Graphing Paper
 5 pcs Color Pen (Different color)
 Ruler