Question

Solve the following equations:
$x-2y+3z=9$
$-x+3y-z=-6$
$2x-5y+5z=17$

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

Answer 1

The correct option is A x=1,y=-1, z=2

$x-2y+3z=9$.....(1)
$-x+3y-z=-6$ ....(2)
$2x-5y+5z=17$......(3)
Let us add equation $1$ and $2$ to eliminate $x$
$x-2y+3z+(-x+3y-z).=9-(-6)$
$y+2z=3$... ...... ....(4)
Now let us solve, equation $1$ and $3$, by multiplying eq.$1$ with $-2$ and adding to eq.$3$
$-2x+4y-6z=-18+(2x-5y+5z=17=-18+17$
$-y-z=-1$ .................(5)
Solve equation $4$ and $5$, we get;
$y+2z=3$
$-y-z=-1$
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$z=\mathrm{2.....}\left(6\right)$
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Substitute the value of $z=2$ in equation $4$
$y+2z=3$
$y+2\left(2\right)=3$
$y=-1$

Now substitute the value of $y$ and $z$ in any of the equations $\left(1\right),\left(2\right),\left(3\right)$
Let us take equation $\left(1\right)$
$x-2y+3z=9$
$x-2(-1)+3\left(2\right)=9$
Solving for x we get,
$x=1$
Therefore, the solution for the given three equation is $(1,-1,2)$