Question

Solve x + y = 5 and 3x + y = 13. Hence find the value of k if 3x + ky = 16.

Answer 1

Given:

x + y = 5

3x + y = 13 

And we want to find the value of (k) such that 3x + ky = 16

Step-wise calculation:

1. From the first equation:

x + y = 5 

⇒ y = 5 – x

2. Substitute (y = 5 – x) into the second equation:

3x + (5 – x) = 13

⇒ 3x + 5 – x = 13

⇒ 2x + 5 = 13

⇒ 2x = 8

⇒ x = 4

3. Substitute (x = 4) back into the first equation to find (y): 

4 + y = 5

⇒ y = 1

4. Now substitute (x = 4) and (y = 1) into the equation (3x + ky = 16): 

3(4) + k(1) = 16

⇒ 12 + k = 16 

⇒ k = 16 – 12

⇒ k = 4

x = 4, y = 1, k = 4

So, the value of (k) is 4.