Question

Can the following system of equations hold simultaneously?

5x + 2y = 26

2x + 3y = 17

3x + 5y = 27

Answer 1

Given the system of equations:

5x + 2y = 26

2x + 3y = 17

3x + 5y = 27

Step-wise calculation:

1. Solve the first two equations for (x) and (y):

Multiply the first equation by 3: 15x + 6y = 78.

Multiply the second equation by 2: 4x + 6y = 34.

Subtract the second from the first:

(15x + 6y) – (4x + 6y) = 78 – 34 

⇒ 11x = 44

⇒ x = 4

Put (x = 4) in the first equation:

5(4) + 2y = 26

⇒ 20 + 2y = 26

⇒ 2y = 6

⇒ y = 3

2. Check the values in the third equation:

3(4) + 5(3)

= 12 + 15

= 27

The third equation is satisfied for x = 4, y = 3.