Question

Explain elimination method with examples

Class 10 ( LiNear equation )

CBSE

Answer 1

In this method,we express one of the variable in terms of the other variable. .
3x+2y=11. as eq.1
2x+3y=4 as eq.2
Let us eliminate y from the given eq.
Coefficient of y in the given eq. is 2 and 3.
lcm of 2 and 3 is 6.so we have to make the coefficient of y equal to 6 in the two eq.
Multiplying eq.1 by 3 and eq.2 by 2
9x+6y=33. as 3eq.
4x+6y=8 as 4eq.
Subtracting eq.4 from 3eq.
5x=25. x=5
put the value of x in eq.1
15+2y=11. 2y=-4. y=-2

Hence the solution of the given system of eq.is x=5 and y=-2

Answer 2

Thanks for asking the question!

ANSWER::

Another name of elimination method is "Addition method' and in this we solve system of equations by which we transform the equation so , the one variable cancels out.

Let us see with some examples :-

Example 1

x -3y = 5

-x+y = 3

Add both equations

x - 3y -x + y = 8 (this thing you have to do in rough column)

-2y = 8

y = -4

To take out value of y put it any of equation like

-x+y = 3

-x -4 =3

-x = 7

x = -7

Answer x = -7 , y = -4

Example 2

x + 3y = -5

4x - y = 6

Now , we have to cancel a variable so , we will multiply the first equation with (-4)

-4x -12y = 20 (after multiplying with -4)

4x - y = 6

Now add both equations

-4x -12y + 4x - y = 20 + 6

-13 y = 26

y = -2

Now take out value of x by putting value of y in equation

4x - y = 6

4x -(-2) = 6

4x + 2 = 6

4x = 6-2

x = 1

Answer x = 1 , y = -2

Hope it helps!