Name:_____________________________
Algebra III
Date: _____________
7-2: Solving Systems of Linear Equations by Elimination Method
Another method that can be used to solve systems of equations is called the______________ or
______________ _______________.
You _____________ both equations by numbers that will allow you to combine the two equations and
___________ ______ of the variables.
Example – Solve the following system using the elimination method.
6x – 3y = –3
4x + 5y = –9
Multiply both sides of the first equation by 5 and the second equation by 3.
Combine the two resulting equations (eliminating the variable y).
Substitute _______ ____________ for x into one of the original equations.
Our computations have produced the point (
,
).
Check the point in the original equations.
First equation,
6x – 3y = –3
Second equation,
4x + 5y = –9
The solution of the system is (
,
).
Solving a System of Linear Equations by the Addition or Elimination Method
1) Rewrite each equation in ___________ form, eliminating fraction coefficients.
2) If necessary, multiply one or both equations by a number so that the _____________ of a chosen variable
are _________________.
3) _______ the equations.
4) Find the ________ of one variable by solving equation from step 3.
5) Find the value of the second variable by ___________ the value found in step 4 into either original equation.
6) Check the proposed solution in the _____________ equations.
Example
Solve the following system of equations using the elimination method.
2
1
3
1
1
𝑥 + 4𝑦 = −2
and
𝑥 − 4 𝑦 = −2
3
2
Multiply both sides of each equation by 12. (Note: you don’t have to multiply each equation by the same
number, but in this case it will be convenient to do so.)
Combine the two equations.
Substitute the value for x into one of the original equations.
Our computations have produced the point (
,
).
Check the point in the original equations. (Note: Here you should use the original equations before any
modifications, to detect any computational errors that you might have made.)
2
1
3
1
1
𝑥 + 4𝑦 = −2
𝑥 − 4 𝑦 = −2
3
2
The solution is the point (
,
).
In a similar fashion to what you found in the last section, use of the ___________ method to combine two
equations might lead you to results like . . .
0 = 0 (which is always true, thus indicating that there are ____________ many solutions, since the two
equations represent the ___________ line), or
0 = 6 (which is ________ true, thus indicating that there are _____ solutions, since the two equations represent
______________ lines).