Elimination Method Algebra

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To solve the system of equations, we need to make the coefficient of one variable as same in both the equations. Then we can eliminate the equal term by using addition or subtraction then we can get a new equation having one variable. Then we can get the value of one variable. After this we can plug value of the one variable then we get the value of another variable.

Example1: Solve the system of equations by using elimination method
                    3x – y = 5
                      x + y = 3

Solution: The given equations are 3x – y = 5 and x + y = 3

We know the y coefficients are equal and having opposite sign
Therefore, we can add the equations


From this we can write x = 2

Now we can plug the value in the equation x + y = 3

2 + y = 3

y = 3 – 2 = 1

(x, y) = (2, 1)
 
Example2: Solve the system of equations by using elimination method
                    2x + 3y = 13
                    3x + 2y = 12

Solution:  First we need to label the given equations

                    2x + 3y = 13    ..................... (1)

                    3x + 2y = 12    ..................... (2)

                    Multiply (1) by 2 and (2) by 3
  Subtract

                           4x + 6y = 26  
                       -   9x + 6y = 36   
                                -
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                             5x    =10     

So, x = 2 plug the x value we can get y = 3.

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