Solving System of Equation by Elimination method
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 (equal but opposite in sign) . The variable can then be eliminated by adding the two equations. This method is also called the Elimination method as it deals straight with getting rid of one of the variables.
Example 1: Solving system of equation by elimination method /Addition method:
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. |
Example 2: At the first meeting of the Chess Club, 12 students were present. After efforts were made to increase interest in the club, twice as many girls and 3 times as many boys attended the second meeting as those that attended the first. If there were 29 students at the second meeting, how many boys and how many girls attended each meeting?
Solution:
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)
Equation (1) was multiplied by -2 to eliminate y
-2x -2y = -24 --------- (3)
adding the two equations
3x + 2y = 29
-2x -2y = -24
_________
X = 5
Plugging x =5 in equation (1)
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
Linear equation in two variables
• Solving linear equation by graphical method.
• Substitution method.
• Solving system of equation by elimination method
• Cross multiplication method or Cramer’s rule