System of linear equations and their solution

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