Question

Solve: $x+2y+z=7$
$x+3z=11$
$2x-3y=11$
Values of x.y and z are respectively

• A. $x=1,y=2,z=3$
• B. $x=2,y=3,z=1$
• C. $x=2,y=1,z=3$
• D. $x=3,y=2,z=1$

Answer 1

The correct option is C $x=2,y=1,z=3$

We have,
$x+2y+z=7$ ...(i)
$x+3z=11$ ...(ii)
$2x-3y=1$ ...(iii)
From equation (i), we get
$z=7-x-2y$
Substituting $z=7-x-2y$ in equation (ii), we get
$x+3(7-x-2y)=11$
$\Rightarrow$ $x+21-3x-6y=11$ .........(iv)
$\Rightarrow$ $-2x-6y=-10$
Adding equation (iii) and (iv), we get
$-9y=-9$

$\Rightarrow$ $y=1$
Putting $y=1$ in equation (iii), we get $x=2$
Putting $x=2,y=1$ in equation (i), we get
$2+2+z=7$

$\Rightarrow$ $z=3$
Hence, $x=2,y=1,z=3$