Question

find the values of x-y, if 5x+4y=14 and 4x+5y=13​

Answer 1

Answer:

x-y =1

Step-by-step explanation:

5x+4y=14____________eqn1

4x+5y=13____________eqn2

multiplying eqn1by 4

20x+16y=56__________eqn3

multiplying eqn2 by 5

20x+25y=65__________eqn4

eqn4 -eqn3

20x+25y=65

20x+16y=56

- - -

_____________

9y=9

y=1

put y =1 in eqn 1

5x+4y=14

5x+4(1)=14

5x+4=14

5x=14-4

5x=10

x=2

x-y= 2-1 =2

Answer 2

Given,

Two equations are 5x+4y=14 and 4x+5y=13

To find,

Value of x-y

Solution,

So we are given two equations in x and y,

We are supposed to find the value of x-y from these two equations.

Let 5x+4y=14 be Equation 1

and 4x+5y=13 be Equation 2

Let's subtract Equation 2 from Equation 1

   (5x+4y=14)

  - (4x+5y=13)

  ⇒(x-y=1) let this be equation 3

Let's add Equation 1 and Equation 2

    (5x+4y=14)

  + (4x+5y=13)

  ⇒(9x+9y=27)

  ⇒(x+y = 3) let this be equation 4

Solve equation 3 and 4.

         (x-y=1)

      + (x+y=3)

      ⇒(2x = 4)

      ⇒ x = 2

Substitute x in equation 3.

2 + y = 3

y = 3-2

y = 1

Hence. the value of (x-y)=1 , values of x and y are 2 and 1 respectively.