Solving system of equation by elimination method can be solved by eliminating one of the variables without solving one variable in terms of the other. The method involves making the coefficients of one the variables the additive inverses

3x + 4y = -1--------------- (1)

6x - 2y = 3---------------- (2)

Step 1:
Decide on the variable to be eliminated |
The variable x can be eliminated by adding the equations if the coefficient of x in equation (1) is changed to -6x. |

Step 2:
Eliminate the variable by suitably multiplying the equations and adding them.
In the above problem the first equation is multiplied by -2. |
Equation(1)*(-2) -6x – 8y = +2 6x – 2y = 3 -------------------- -10 y = 5 y = 5 / -10 ( dividing both sides by -10) y = - ½ |

Step 3:
Plug in the value of y found in any one of the given equations and solve for x |
Plugging y = `-1/2` in equation (1) 3x + 4( -1/2) = -1 3x + (-2) = -1 3x = +1 Transposing -2 to the right side x = `1/3` Dividing by 3 and simplifying |

Check:
Plug the values of x and y found in equation (2) and check whether the equation Is satisfied. |
6 x (1/3) - 2 x (-1/2) = 3 2 + 1 = 3 The equation is satisfied. |

Let the number of boys and girls in the first meeting be x and y respectively.

X + y = 12--------------(1)

No of boys in the second meeting = 3x

No of girls in the second meeting = 2y

Total number of students = 29.

3x + 2y = 29-----------(2)

-2x -2y = -24 --------- (3)

adding the two equations

3x + 2y = 29

-2x -2y = -24

_________

X = 5

5 + y = 12 ⇒ y =7

No of boys who attended the first meeting = 5

No of girls who attended the first meeting = 7

No of boys who attended the second meeting = 15

No of girls who attended the second meeting = 14

• Solving linear equation by graphical method.

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