Elimination Method in System of Linear Equation In Two Variables. Grade 8 Mathematics.

1. Elimination
Method:
Linear
Equation
Math 8
-Keizar

5. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1

6. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1
2. 12x + 4y = 48 x = 0 y = 0

7. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1
2. 12x + 4y = 48 x = 0 y = 0
3. 4x – 2y = 12 x = 2 y = 4

8. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1
2. 12x + 4y = 48 x = 0 y = 0
3. 4x – 2y = 12 x = 2 y = 4
4. 5y – 3x = 60 x = 0 y = 0

9. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1
2. 12x + 4y = 48 x = 0 y = 0
3. 4x – 2y = 12 x = 2 y = 4
4. 5y – 3x = 60 x = 0 y = 0
5. x – y = 24 x = -4 y = 0

10. Basic Skills
1. 2x + 3y = 21 x = 0 y = 1 (0,7) and (9,1)
2. 12x + 4y = 48 x = 0 y = 0 (0,12) and (4,0)
3. 4x – 2y = 12 x = 2 y = 4 (2,-2) and (5,4)
4. 5x – 3y = 60 x = 0 y = 0 (0,-20) and (12,0)
5. x – y = 24 x = -4 y = 0 (6,18) and (24,0)

11. Elimination Method
The elimination method is where you actually eliminate one of the variables by
adding the two equations. In this way, you eliminate one variable so you can solve for
the other variable. In a two-equation system, since you have two variables, eliminating
one makes the process of solving for the other quite easy.

12. Objectives:
Apply the substitution principle to check
whether the answer/s is/are correct
Solve system of linear equation in two variables
by elimination method

13. Graphing System Of Linear Equation In 2
Variables
2x + 4y = 6 1st Equation
4x + y = 8 2nd Equation
Intercept Method
1st Equation
2x + 4y = 6
2x + 4(0) = 6
2x = 6
x = 3 (3,0)
2(0) + 4y = 6
0 + 4y = 6
y = or
(0, )
(3,0)
(0,3/2)
2nd Equation
4x + y = 8
4x + (0) = 8
4x = 8
x = 2 (2,0)
4x + y = 8
4(0) + y = 8
0 + y = 8
y = 8
(0,8)
(2,0)
(0,8)
Point of
Intersection
It has one
solution.

14. Steps In Solving Systems Of Linear Equation
By Elimination Method
Standard Form: Ax + By = C
(they must be in standard form, and they must be in the same form)
Decide which
variable you want
to eliminate.
Multiply one or both
equation by the
appropriate constant so
that the variable that you
want to eliminate
becomes additive inverse
of each other.
Add the resulting
equation.
Solve the equation
obtained in Step 3
Substitute the value of the
variable obtained in Step
4 into one of the original
equations and solve for
the other variable.
Check your
solution in both
original equations.

15. Additive Inverse
-Same coefficient
-Opposite Sign.
2x + 3y = 6
4x – 3y = 8
Identify if there is an additive inverse.
if there is no Additive Inverse, you need to
have Additive Inverses by multiplying.
-2x + 3y = 16
2x – 4y = 20
7x + y = 12
9x – y = 10
2x + 4y = 6
4x – 3y = 8
Do the Step 1 and 2.
If you choose to eliminate x
Think of a number that if
you multiply, you will get
Same Coefficient and
Opposite Sign
(-2)
If we multiply the -2 in 2x
we get –4x. Remember:
You need to multiply the
whole equation.
-4x -8y = -12
4x -3y = 8
If you choose to eliminate y
2x + 4y = 6
4x – 3y = 8
(3)
(4)
6x +12y = 18
16x – 12y = 32

16. Solving System Of Linear Equation Ny
Elimination Method
x + y = 8
x – y =2
x + y = 8
x – y = 2
2x = 10
2
x = 5
5 + y = 8
5-5 + y = 8 – 5
y = 3
5 – y = 2
5-5 –y = 2 – 5
(-y = -3)(-1)
y = 3
Checking
x = 5
y = 3
Equation 1
5 + 3 = 8
8 = 8
Equation 2
5 – 3 = 2
2 = 2
Since (5, 3) satisfies both
equation then it is the solution
to the system
The system is consistent, and
the equation are independent. It
has one solution.

17. Solving System Of Linear Equation By
Elimination Method
3x + 4y = 4
(x – 2y =2)
3x + 4y = 4
-3x + 6y = -6
10y = -2
10
y = -1/5
x – 2y = 2
x – 2(-1/5) = 2
x + 2/5 = 2
x = 2 – 2/5
x = 8/5
Checking
x = 8/5
y = -1/5
Equation 1
3(8/5) + 4(-1/5)
24/5 – 4/5 = 4
20/5 = 4
4 = 4
Equation 2
8/5 – 2(-1/5) = 2
8/5 + 2/5 = 2
10/5 = 2
2 = 2
-3

18. Solving System Of Linear Equation By
Elimination Method
Find the LCD of this fraction
2x – 3y = -2
2x – 3y = -2

19. Solving System Of Linear Equation By
Elimination Method
Checking
Equation 1 Equation 2

20. Formative Assessment

21. Formative Assessment

22. Formative Assessment

23. Formative Assessment

24. Formative Assessment