Question

If 15x + 17y = 23 & 17x + 15y = 41 then (5x+5y)=________.​

Answer 1

EXPLANATION.

⇒ 15x + 17y = 23. - - - - - (1).

⇒ 17x + 15y = 41. - - - - - (2).

As we know that,

Whenever we see this type of linear equations where coefficients of x and y are interchanging with each other then first we adding both the equations then we subtracting both the equations, we get.

Adding both the equations, we get.

⇒ 15x + 17y = 23. - - - - - (1).

⇒ 17x + 15y = 41. - - - - - (2).

We get,

⇒ 32x + 32y = 64.

⇒ x + y = 2. - - - - - (3).

Subtracting both the equations, we get.

⇒ 15x + 17y = 23. - - - - - (1).

⇒ 17x + 15y = 41. - - - - - (2).

⇒ -      -          -

We get,

⇒ - 2x + 2y = - 18.

⇒ - x + y = - 9. - - - - - (4).

Now, we solving equation (3) and equation (4), we get.

Adding both the equations, we get.

⇒ x + y = 2. - - - - - (3).

⇒ - x + y = - 9. - - - - - (4).

We get,

⇒ 2y = - 7.

⇒ y = -7/2.

Put the value of y = -7/2 in equation (3), we get.

⇒ x + y = 2. - - - - - (3).

⇒ x + (-7/2) = 2.

⇒ x - 7/2 = 2.

⇒ x = 2 + 7/2.

⇒ x = (4 + 7)/(2).

⇒ x = 11/2.

Values of : x = 11/2  and  y = -7/2.

To find : 5x + 5y.

⇒ 5x + 5y = 5(11/2) + 5(-7/2).

⇒ 5x + 5y = 55/2 - 35/2.

⇒ 5x + 5y = (55 - 35)/(2).

⇒ 5x + 5y = 20/2.

⇒ 5x + 5y = 10.

∴ The value of 5x + 5y = 10.

Answer 2

given

15x + 17y = 23 ———(1)

17x + 15y = 41 ———(2)

Now adding (1) & (2) we get

32x + 32 y =64

x + y =2

multiplying both sides by 5

5(x + y) =5×2

5x + 5y = 10