Question

Solve

$5x-y-z=(-2)$
$3x+y-2z=(-5)$
$x-y+3z=14$

Answer 1

Solution:-

$5x-y-z=-2.....\left(i\right)$

$3x+y-2z=-5.....\left(ii\right)$

$x-y+3z=14.....\left(iii\right)$

Adding ${eq}^n\left(i\right)\&\left(ii\right)$, we have

$(5x-y-z)+(3x+y-2z)=(-2)+(-5)$

$8x-3z=-7.....\left(iv\right)$

Again, adding ${eq}^n\left(ii\right)\&\left(iii\right)$, we have

$(3x+y-2z)+(x-y+3z)=(-5)+14$

$4x+z=9.....\left(v\right)$

Multiplying ${eq}^n\left(v\right)$ by 3, we get

$12x+3z=27.....\left(vi\right)$

Adding ${eq}^n\left(iv\right)\&\left(vi\right)$, we have

$(8x-3z)+(12x+3z)=(-7)+27$

$20x=20$

$x=1$

Substituting the value of x in ${eq}^n\left(v\right)$, we have

$4\times 1+z=9$

$\Rightarrow z=9-4$

$\Rightarrow z=5$

Substituting the value of $x$ and $z$ in ${eq}^n\left(i\right)$, we have

$5\times 1-y-5=-2$

$\Rightarrow 5-y-5=-2$

$\Rightarrow y=2$

Hence, for the given pair of lines, $x=1,y=2,z=5$.