Elimination Method

ELIMINATION METHOD:

Algorithm to find the solution:

Step 1: If coefficients of one variable ( either x or y ) in both the equations are not equal, then first multiply both the equations by some suitable non-zero constants to make the coeffiecients of one variable ( either x or y ) numerically equal.

Step 2: Add or subtract one equation from the other so that one variable gets eliminated.If you get an equaton in one variable, go to Step 3.

If in step 2, we obtain a true statement involving no variable, then the original pair of equations has infinitely many solutions.

If in step 2, we obtain a false statement involving no variable, then the original pair of equations has no solution, i.e., it is the given system is inconsistent.

Step 3: Solve the equation in one variable (x or y) so obtained to get its value.

Step 4: Susbtitute this valur of variable (x or y) in either of the original equations to get the value of the other variable.

Example : The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.

SOLUTION :

Let the incoome of the two person be Rs. 9x and Rs. 7x and their expenditures be Rs. 4y and Rs. 3y respectively. Then the equations formed for the given situation are given by :

9x - 4y = 2000 ............(i)

and 7x - 3y = 2000 .............(ii)

Step 1: Multiply Equation (i) by 3 and Equation (ii) by 4 to make the coefficients of y equal. Then we get the equations:

27x - 12 y = 6000 .........(iii)

28x - 12y = 8000 .........(iv)

Step 2: Subtract Equation (iii) from Equation (iv) to eliminate y, because the coefficients of y are the same. So, we get

(28x - 27x) - (12y - 127) = 8000 - 6000

i.e., x = 2000

Step 3: Subtituting this value of x in (i), we get

9(2000) - 4y = 2000 i.e.., y = 4000

So, the solution of the equations: x = 2000, y = 4000. Therefore, the monthly incomes of the two persons are Rs. 18,000 and Rs. 14000, respectively.

Verification : 18000 : 14000 = 9 : 7.

Also, the ratio of their expenditures = 18000 - 2000 : 14000 - 2000 = 16000 : 12000 = 4 : 3

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Aruna has only Re 1 and Rs 2 coin with her. If the total number of coin that she has is 50 and the amount of money with her Rs 75 , then the number of Re 1 and Rs 2 coin are,respectively .
A. 35 and 15	B. 35 and 20	C. 15 and 35	D. 25 and 25
Right Option : D
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Question : 2

The father's age is six times his son's age . Four years hence,the age of the father will be four times his son's age . The present ages, in years, of the son and the father are , respectively
A. 4 and 24	B. 5 and 30	C. 6 and 36	D. 3 and 24
Right Option : C
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Question : 3

Solve the system of equation 2x + y = - 4 and 5x – 3y = 1 by the method of elimination.
A. x = 2 and y = -2	B. x = -2 and y = -2	C. x = -1 and y = -2	D. x = -1 and y = -1
Right Option : C
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