Question

Solve the following system of linear equations in three variables.
2x - 7y + 11z = 0
6x - 8y + 7z = 0
3x + 4y + 5z = 35

• A. x = 1, y = 2, z = 3
• B. x = 0, y = 4, z = 1
• C. x = 3, y = 4, z = 2
• D. x = - 1, y = 2, z = 1

Answer 1

The correct option is C x = 3, y = 4, z = 2

2x - 7y + 11z = 0 .....(1)
6x - 8y + 7z = 0 .....(2)
3x + 4y + 5z = 35 ....(3)

$\Rightarrow eqn\left(1\right)\times 3-eqn\left(2\right)$

$6x-21y+33z=0$
$-6x+8y-7z=0$
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$-13y+26z=0$
$-y+2z.....................\left(4\right)$

$\Rightarrow eqn\left(2\right)-2\times eqn\left(3\right)$

$6x-8y+7z=0$
$-6x-8y-10z=-70$
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$-16y-3z=-70$
$16y+3z=\mathrm{70.....................}\left(5\right)$

$\Rightarrow eqn\left(4\right)\times 16+eqn\left(5\right)$

$-16y+32z=0$
$16y+3z=70$
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$35z=70$
$z=\mathrm{2.....................}\left(6\right)$

Substituting eqn(6) in eqn(4),we get,

$-y+2\left(2\right)=0$
$-y=-4$
$y=\mathrm{4.....................}\left(7\right)$

Substituting eqn(6) and eqn(7) in eqn(1), we get

$2x-7\left(4\right)+11\left(2\right)=0$
$2x-14+22=0$
$2x-6=0$
$2x=6$
$x=3$