The document discusses using the elimination method to solve systems of linear equations by eliminating one variable, substituting values into the original equations to solve for the remaining variable, and checking that the solutions satisfy both equations. It provides step-by-step examples of using the elimination method to solve two systems of linear equations, eliminating variables by adding or multiplying equations. The document concludes with practice problems for students to solve systems of linear equations using the elimination method.

1. Systems of Linear
Equations
Solving Systems of Linear Equation
Using Elimination Method

2. Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile

3. Objectives:
• recall inverse property of addition
• recall addition property of equality
• recall multiplication property of
equality
• recall substitution method
• use elimination method
• find the solution of the systems of
linear equations

4. Steps in eliminating of the unknowns:
1. Compare the coefficients of
the variable you wish to
eliminate. If they have the same
coefficients, then eliminate
them by either adding or
subtracting.
2. If the coefficients of the
variable to be eliminated are
different. Multiply one equation
or both equations with an
appropriate number that would
make the coefficients the same.
Then eliminate the variable
either by adding or subtracting.
3. Solve the resulting linear
equation in one unknown.
4. Substitute the value obtained
into any of the original
equations to solve for the other
variable.
5. Check whether or not the
values satisfy both equations.

5. Examples1:
Solution:
Step 1: Add the two equations to
eliminate y. (The coefficients of y
are opposites.)Then solve for x.
x + 2y = 8
+ 3x – 2y = 8
4x = 16
x = 4
Solve the system using
the elimination method.
x+ 2y =8 Equation 1
3x – 2y = 8 Equation 2

6. Examples1:
Solution:
Step 2: Substitute 4 for x in either
of the equations, then solve for y.
Equation 1: x + 2y = 8
4 + 2y = 8
2y = 4
y = 2
The solution is (4, 2)
Solve the system using
the elimination method.
x+ 2y =8 Equation 1
3x – 2y = 8 Equation 2

7. Examples 2:
Solution:
Step 1. Multiply eq.1 by 3 and equation 2 by -2 to make the coefficient of
x opposites.
(2x + 3y = 15) 6x + 9y = 45
(3x + 2y = 5) -6x – 4y = -10
Solve the system using the elimination method.
2x + 3y = 15 Equation 1
3x + 2y = 5 Equation 2
Step 2. Add the two equations to eliminate x, then solve for y.
6x + 9y = 45
+ -6x – 4y = -10
5y = 35
y = 7

8. Examples 2:
Solution:
Step 3. Substitute 7 for y in either of the equations 1 or 2, then solve for x.
Equation 1: 2x + 3y = 15
2x + 3(7) = 15
2x + 21 = 15
2x = 15 – 21
2x = -6
x = -3
The solution is ( -3, 7 )
Solve the system using the elimination method.
2x + 3y = 15 Equation 1
3x + 2y = 5 Equation 2

9. To Do…
Solve the following systems of linear equations by
eliminations:
1. x + y = 14 and x – y = 2
2. 2m – n = 3 and m + n = 9
3. x + y = 2 and 2x – y = 10

10. Thank you!

11. Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module