Question

4x +3y = 11 ; 3x + 4y = 10

Answer 1

x = 2 ; y = 1

Explanation:

GIVEN :-

• 
  `4x + 3y = 11` (eqn.1)
• 
  `3x + 4y = 10` (eqn.2)

SOLUTION :-

The easiest way to solve such questions where two linear equations (with two variables) ax + by = c and bx + ay = d are given is :-

1) Add both the equations :-

`4x + 3y + 3x + 4y = 11 + 10`

`=> 7x + 7y = 21`

Simplify it further.

`7(x + y) = 21`

`=> x + y = (21)/(7) = 3` ..... eqn.3

2) Substract both the equations :-

`4x + 3y - 3x - 4y = 11 - 10`

`=> x - y = 1` ..... eqn.4

3) Now add eqn.3 and eqn.4 to get the value of 'x' :-

`x + y + x - y = 3 + 1`

`=> 2x = 4`

`=> x = (4)/(2) = 2`

4) Substitute the value of 'x' in either eqn.1 or eqn.2 and solve it to get the value of 'y' ( I'm here substituting it in eqn.1 ) :-

`4 * 2 +3y = 11`

`=> 3y = 11 - 8 = 3`

`=> y = (3)/(3) = 1`