Question

Solve
x + 6y - 5z = 0
7x + z = 6y
5x + 6y - 4z = 24

• A. x = 2, y = 1, z = 3
• B. x = 1, y = 2, z = 3
• C. x = 4, y = 6, z = 8
• D. x = 3, z = 1, y = 2

Answer 1

The correct option is C x = 4, y = 6, z = 8

x + 6y - 5z = 0 ....(1)
7x + z - 6y = 0 ....(2)
5x + 6y - 4z = 24 ....(3)

eqn(1) + eqn(2) gives

x+6y-5z=0
7x-6y+z=0
______________
8x-4z=0
2x-z=0-----------(4)

eqn(1) - eqn(3) gives

x + 6y - 5z = 0
-5x - 6y + 4z = -24
____________
-4x-z=-24
4x+z=24 -----------(5)

eqn(4) - eqn(5) gives

6x = 24
x = 4-------------(6)

Subtracting eqn(6) in eqn(4) we get

$2\times 4-z=0$
$z=8$-----------(7)

Subtracting eqn(6) and eqn(7) we get

4 + 6y - 40 = 0
6y = 36
y = 6-----------(8)

Now,
substituting the values of x,y and z we get in eqn (3)

$LHS=5\times 4+6\times 6-4\times 8$
$=20+36-32$
$=24$
$=RHS$