System of Linear equations in two
variables
Solving system of linear equations by
elimination method
NAME: ________________________________________
GRADE AND SECTION: ___________________________
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I. Objectives
At the end of the 60 minute session the learners are expected to;
1.) Solves system of linear equations in two variables by elimination method.
2.) Boast their confidence in solving system of linear equations in two variables using
elimination method.
3.) Develop their speed and accuracy in solving system of linear equations in two
variables by elimination method.
Motivation Part:
What should be added to the following numbers to make it zero?
1.) -1 + _____ = 0
2.) 100 + ____ = 0
3.) x + ______ = 0
4.) –y + _____ = 0
5.) 2x + _____ = 0
What did you learn?
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LESSON PART:
What is Elimination method?
This method involves eliminating one of the variables by adding a multiple of one
equation to the other equation. Once a variable has been eliminated in this manner, we
then solve for the remaining variable and use that value to solve for the eliminated
variable.
(Example 1)
Let’s solve this system of Linear equations by elimination:
3x – y = 2 (1)
4x + y = 5 (2)
2
Instruction: Follow the steps in Elimination method to find the value for x and y.
Step one
Look at the equations!
3x – y = 2
4x + y = 5
Are they both in standard form?
Ax + By = C
YES
NO
Rewrite equations
Rewrite the equations in standard
from
Ax + By = C
Step two
Look at the equations!
3x – y = 2
4x + y = 5
Are there any equal and opposite
variables?
YES
Multiply the equation(s)
Multiply one or both equations by a
non-zero number to create a pair of
equal and opposite variables.
NO
Step three
Add together the two equations to make
a single equation with one variable.
Step six
Check the solutions.
Step four
Solve the equation from step 3.
Step five
Solve the value for the
variable you just solved into
one of the equations.
3
(Example 2) Let’s solve this system of Linear equations by elimination:
Step one
Look at the equations!
y = x -3 (1)
2x + y =3 (2)
Are they both in standard form?
Ax + By = C
YES
NO
Rewrite equations
Rewrite the equations in standard
from
Ax + By = C
Step two
Look at the equations!
Are there any equal and opposite
variables?
YES
Multiply the equation(s)
Multiply one or both equations by a
non-zero number to create a pair of
equal and opposite variables.
NO
Step three
Add together the two equations to make
a single equation with one variable.
Step six
Check the solutions.
Step four
Solve the equation from step 3.
Step five
Solve the value for the
variable you just solved into
one of the equations.
4
TRY YOURSELF! Solve the given System of Linear equations to find the value of x and y.
Step one
Look at the equations!
x + 2y = 9 (1)
x – 2y = 5 (2)
Are they both in standard form?
Ax + By = C
YES
NO
Rewrite equations
Rewrite the equations in standard
from
Ax + By = C
Step two
Look at the equations!
Are there any equal and opposite
variables?
YES
Multiply the equation(s)
Multiply one or both equations by a
non-zero number to create a pair of
equal and opposite variables.
NO
Step three
Add together the two equations to make
a single equation with one variable.
Step six
Check the solutions.
Step four
Solve the equation from step 3.
Step five
Solve the value for the
variable you just solved into
one of the equations.
5
Evaluate Yourself!
Solve the given System of Linear equations to find the value of x and y.
Step one
Look at the equations!
𝒚 = −𝒙 + 𝟓 (1)
𝟐𝒙 − 𝒚 = −𝟐 (2)
Are they both in standard form?
Ax + By = C
YES
NO
Rewrite equations
Rewrite the equations in standard
from
Ax + By = C
Step two
Look at the equations!
Are there any equal and opposite
variables?
YES
Multiply the equation(s)
Multiply one or both equations by a
non-zero number to create a pair of
equal and opposite variables.
NO
Step three
Add together the two equations to make
a single equation with one variable.
Step six
Check the solutions.
Step four
Solve the equation from step 3.
Step five
Solve the value for the
variable you just solved into
one of the equations.
6