Question

If 5x + 4y = 13 and 4x + 5y = 14, find the value of (x - y).​

Answer 1

Given :-

• 5x + 4y = 13 => Equation 1
• 4x + 5y = 14 => Equation 2

To find :-

(x-y)

Equation 1 :

5x + 4y = 13

5x = 13 - 4y

$x = \dfrac{13 - 4y}{5}$

Substituting the value in Equation 2,

Equation 2 :

4x + 5y = 14

$4 \bigg( \dfrac{13 - 4y}{5} \bigg) + 5y = 14$

$\dfrac{52 - 16y}{5} + 5y = 14$

LHS (Left hand side) Lcm = 5

$\dfrac{52 - 16y + 5y(5)}{5} = 14$

$\dfrac{52 - 16y + 25y}{5} = 14$

$\dfrac{52 + 9y}{5} = 14$

Transposing 5 to the RHS (Right Hand Side),

52 + 9y = 14(5)

52 + 9y = 70

Transposing 52,

9y = 70 - 52

9y = 18

$y = \dfrac{18}{9}$

$y = 2$

Therefore,

$x = \dfrac{13 - 4y}{5}$

$x = \dfrac{13 - 4(2)}{5}$

$x = \dfrac{13 - 8}{5}$

$x = \dfrac{5}{5} = 1$

Verification:-

Substituting x for 1 and y for 2,

Equation 1 :

5x + 4y = 13

5(1) + 4(2) = 13

5 + 8 = 13

LHS = RHS

Equation 2 :

4x + 5y = 14

4(1) + 5(2) = 14

4 + 10 = 14

LHS = RHS

Hence verified

(x-y) :-

1 - 2

= (-1)

Answer :- (-1)

Answer 2

Answer:

x-y=-1

Step-by-step explanation:

above method is right