Question

k-1)x+(k-1)y=17 (K-1)x+(k-2)y=18 X+y =5

Answer 1

Answer:

x = 6 and y = -1

Step-by-step explanation:

The equations given to us are:

1. (k-1)x + (k-1)y = 17
2. (k-1)x + (k-2)y = 18
3. x+y = 5

Let us begin by simplifying the 1st equation:

(k-1)x + (k-1)y = kx - x + ky - y

⇒ kx - x + ky -y = 17

⇒ k (x+y) - 1(x+y) = 17

Putting the value of x+y from the 3rd equation, we get,

k (5) - 1 (5) = 17

⇒ 5k - 5 = 17

⇒ 5k = 22

⇒ k = 22/5

Now, let us simplify the 2nd equation in the similar pattern:

(k-1)x + (k-2)y = kx - x + ky - 2y

⇒ kx - x + ky - 2y = 18

⇒ k (x+y) - x - 2y = 18

⇒ k (5) - x - 2y = 18 (∵ x+y = 5 from the 3rd equation)

Putting k= 22/5 in the above equation, we have,

$5 * \frac{22}{5} - x - 2y = 18$

⇒ 22 - x - 2y = 18

⇒ 22 - 18 = x+2y

⇒ x+2y = 4

Subtracting the above equation from the 3rd equation, we have,

x+y - (x+2y) = 5 - 4

⇒ x + y - x - 2y = 1

⇒ -y = 1

⇒ y = -1

Putting y = -1 in equation 3, we have,

x - 1 = 5

⇒ x = 6

Thus, x=6 and y = -1 is the solution.