SOLVING LINEAR EQUATION USING ELIMINATION METHOD… July 7, 2008

1) 3x – y = 5 and 5x + 2y =12

Using Elimination Method

Step 1. If the two equations doesn’t have any additive inverse, multiply one or both equation by a number so that it will have an additive inverse. In this example we will multiply the 1st equation by 2.

(3x – y = 5)2 ——-> 6x – 2y = 10

Step 2. Now that the two equations have an additive inverse, you can eliminate one of the variables by adding the two equations.

6x - 2y = 10 Note: The numbers and variable in bold will be added while the

5x + 2y = 12 variables in Italics will be eliminated.

11x = 22 Divide by 11

x = 2

Step 3. To solve for y, substitute 2 for x, using any of the equation.

3x – y = 5

3(2) -y = 5 Substitute x = 2

6 – y = 5

- y = 5 – 6 Transpose 6

- y = – 1 Divide both side by -1

y = 1

Step 4. Check.

3x – y = 5 l 5x + 2y = 12

3(2) – 1 = 5 l 5(2) +2(1) = 12

6 – 1 = 5 l 10 + 2 = 12

5 = 5 l 12 = 12

therefore the solution is (2, 1)

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