Question

The value of $x,y$ and $z$ respectively, on simplifying the equations $2x+3y=0,3y+4z=14,2x+4z=26$ is

• A. $3,-2,5$
• B. $-3,2,5$
• C. $-3,2,-5$
• D. $3,2,5$

Answer 1

The correct option is A $3,-2,5$

$2x+3y=0$ ..... $\left(i\right)$

$3y+4z=14$ ...... $\left(ii\right)$

$2x+4z=26$ ..... $\left(iii\right)$

From the first equation, $3y=-2x$.
Substituting this in $2^{nd}$ equation, it becomes $4z-2x=14$
Adding the $2^{nd}$ and $3^{rd}$ equations, we get
$8z=40$.
Therefore, $z=5$.
Substituting this in $2^{nd}$ equation, we get $3y=14-5.4$
we get $y=-2$.
Substituting this in $1^{st}$ equation, we get $x=3$.
Therefore, $(x,y,z)=(3,-2,5)$.