Question

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

Answer 1

Answer:

x = 2 ; y = 1

Step-by-step 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.

$7(x + y) = 21$

$=> x + y = \frac{21}{7} = 3$ ..... 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' :-

$x + y + x - y = 3 + 1$

$=> 2x = 4$

$=> x = \frac{4}{2} = 2$

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 ) :-

$4 \times 2 +3y = 11$

$=> 3y = 11 - 8 = 3$

$=> y = \frac{3}{3} = 1$