Elimination is another method used for

solving systems of linear equations.

Most people consider this method the

easiest. I hope you find it easy, too! To

help explain this method, I will use the

example :

4x -3y = 0

-10x +7y = -2

 

 

In the first step, one or both of the equations are to be multiplied by a constant to obtain co-efficients ( for any one of the two variables ) that differ in sign only. While multiplying, remember to multiply both sides by the same number!
  • The two equations :
    +04x -3y = 0
    -10x +7y = -2
  • If the first equation is multiplied by 10 and the second equation is multiplied by 4, then the coefficients of x will be same except for their sign.
  • ( 10 ) 4x - 3y = 0 ( 10 ) ===>> 40x- 30 y = 0
  • (4) -10 x + 7y = -2 (4) ===>> - 40x + 28 = -8
In the second step, the two equations are added. Step one allows one of the two variables to be cancelled out. Afterwards, the remaing value is to be solved for.

+40 x - 30y = 0
- 40 x + 28y = -8
_____________________
0 x - 2y = -8
y = 4
In the third step, the value found is to be substituted into any one of the equations to find the value of the other variable..
  • Value of y : y = 4
  • First equation : 4x - 3y = 0
  • Substitute value of y : 4x - 3 (4) = 4
  • Solve for x :
    4x - 3 (4) = 0
    4x = 12
    x = 3

In this way, the value of x and y are found by using the elimination method.

x = 3 , y = 4

 

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