MPM1DW
Date: _____________________
The second ‘algebraic’ method of solving systems is called elimination.
In elimination, we add or subtract two equations with the goal being to eliminate one of the variables.
Here is a simple example, to show you how it works:
x y 6
x y 4
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+ 2 x  0  10
x5
Sub x = 5 into 
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x  y 6
Therefore, the solution to the system is (5, 1).
5 y  6
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y1
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Another way to have solved this system using a similar idea would be:
x y 6
x y 4
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
- 0  2 y  2
y 1
Sub y = 1 into 
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 x y 6
x1 6
x5
Therefore, the solution to the system is (5, 1).
Steps for solving equations by using elimination:
1. Equations must be lined in the form
Ax  By  C 
 (Rearrange if necessary)
Dx  Fy  G 
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2.
If A and D, or B and F are the same coefficient, subtract the two equations.
If A and D, or B and F are opposite coefficients, add the two equations.
*This step will eliminate a variable*
3.
Solve the simple equation for the remaining variable.
4.
Sub the solution from step 3 back into equation  or . Then, solve for the other unknown.
5.
State your solution in (x, y) form.
6.
Check if asked
Ex 1
Solve the following systems of equations by elimination
a) 3 x  2 y  19      b)
2a  3b  7 
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5x  2 y  5
5b  2a  9
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c)
4c  3d  8 
  8
 d 
4c 
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