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Elimination Method

Pair of Linear Equations II - Concepts

Solving Pair of Linear Equation Using Substitution

Elimination Method

Cross Multiplication Method

Class - 10th IMO Subjects

Concept Explanation

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

Find the value of x and y : $large 217x+131y=913$ and $large 131x+217y=827: is$
A. $x=2,y=3$		B. $x=3,y=2$
C. $x=2,y=2$		D. $x=3,y=3$
Right Option : B
View Explanation

Question : 2

If $large 3x+4y:x+2y:4,$ then $large 3x+5y:3x-y$ is equal to
A. 4:1	B. 1:4	C. 7:1	D. 1:7
Right Option : C
View Explanation

Question : 3

Solve the system of equation 2x + 3y = 11, x + 2y = 7 by the method of elimination.
A. x = -1 and y = -3	B. x = 1 and y = -3	C. x = -1 and y = 3	D. x = 1 and y = 3
Right Option : D
View Explanation