Question

If the system of the following equations hold simultaneously, find the value of k.

4x + 3y = 11

x – y = 1

3x + ky = 10

Answer 1

Given:

4x + 3y = 11

x – y = 1

3x + ky = 10

Step-wise calculation:

1. From the second equation, express (x) in terms of (y):

x = y + 1

2. Substitute (x = y + 1) into the first equation:

4(y + 1) + 3y = 11

4y + 4 + 3y = 11

7y + 4 = 11

7y = 7

y = 1

3. Find (x) using (x = y + 1):

x = 1 + 1

x = 2

4. Use (x = 2) and (y = 1) in the third equation to find (k):

3(2) + k(1) = 10

6 + k = 10

k = 10 – 6

k = 4

The value of (k) is 4.