Question

Solve 3x – 2y = 1 and 2x + 5y = 7. Hence find the value of k if 2x + 7y = k.

Answer 1

Given: 3x – 2y = 1 and 2x + 5y = 7

Step-wise calculation:

1. Multiply the first equation by 5 and the second equation by 2 to align the coefficients of (y): 

5(3x – 2y) = 5 × 1

⇒ 15x – 10y = 5

 2(2x + 5y) = 2 × 7

⇒ 4x + 10y = 14

2. Add the two equations to eliminate (y):

(15x – 10y) + (4x + 10y) = 5 + 14

⇒ 19x = 19

⇒ `x = 19/19`

⇒ x = 1

3. Put (x = 1) in the second original equation:  

2(1) + 5y = 7 

⇒ 2 + 5y = 7

⇒ 5y = 5

⇒ y = 1

4. Now, find (k) in the equation:

2x + 7y = k

Put (x = 1) and (y = 1): 

2(1) + 7(1) = 2 + 7

2(1) + 7(1) = 9 

So, k = 9.