Elimination

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Example: Find the P.O.I. by elimination forand 9 yx 624 yx

Steps Example

1a. Rearrange one (or both) of the equations so that the x’s and the y’s are one the same side (left or right) for both equations

 

 x + y = 9

4x – 2y = -6

Example: Find the P.O.I. by elimination forand 9 yx 624 yx

1b. Line up both equations and decide which one the variables (x or y) you are going to eliminate.

  x + y = 9

4x – 2y = -6

*You could choose to eliminate either the x’s or the y’s. We will eliminate the y’s.

Example: Find the P.O.I. by elimination forand 9 yx 624 yx

1c. If you need to, multiply one or both equations by a number to make the coefficients match for the variable you’re going to eliminate. 

 (x + y = 9) 2

2x + 2y = 18

4x – 2y = -6

Example: Find the P.O.I. by elimination forand 9 yx 624 yx

2. Eliminate the variable by either adding or subtracting the second equation from the first.

Solve for the remaining variable.

  

 

  2x + 2y = 18

+ 4x – 2y = -6

6x + 0y = 126x = 12 x = 12 x = 2 

 

Example: Find the P.O.I. by elimination forand 9 yx 624 yx

3. Substitute the value for the variable, which was found in step 2 into one of the original equations and solve for the other variable.

  x + y = 9

Sub in “2” for “x”

2 + y = 9

y = 9 – 2

y = 7

 

 

Example: Find the P.O.I. by elimination forand 9 yx 624 yx

4. Verify your answer by substituting the value in step 3 into the other original equation.

 (2, 7)

Substitute “2” in for “x” and “7” in for “y” in the equation: 4x = 2y – 6

4(2) = 2(7) – 6

8 = 14 – 6

8 = 8

The POI is (2, 7)