Question

If the system of linear equations

x – 4y + 7z = g

3y – 5z = h

–2x + 5y – 9z = k is consistent, then:
1. g + 2h + k = 0
2. g + h + 2k = 0
3. 2g + h + k = 0
4. g + h + k = 0

Answer 1

Correct Answer - Option 3 : 2g + h + k = 0

The given system of linear equations is:

x – 4y + 7z = g     ----(1)

3y – 5z = h     ----(2)

–2x + 5y – 9z = k     ----(3)

On multiplying equation (i) by 2,

2x – 8y + 14z = 2g     ----(4)

Adding equation (2), equation (3) and equation (4), we get

⇒ 3y – 5z – 2x + 5y – 9z + 2x – 8y + 14z = h + k + 2g

⇒ 0 = 2g + h + k

∴ 2g + h + k = 0

Then, the system of equation is consistent.