Question

Please show work! I don't understand how this problem works!!! I will give branliest for best answer!

Answer 1

Answer:

The point is $(2,-2,1)$.

Step-by-step explanation:

Given:

The set of equations are:

$x+y-z=-1\\4x-3y+2z=16\\2x-2y-3z=5$

Multiply equation 1 by 2, we get

$(x+y-z=-1)\times 2=2x+2y-2z=-2$ ----- 4

Add equations 3 and 4.

$2x-2y-3z=5\\2x+2y-2z=-2$

$(2x+2x)+(-2z-3z)=-2+5\\4x-5z=3$

So, we got a new equation as $4x-5z=3$-------- 5

Now, we multiply equation 1 by 3, we get

$(x+y-z=-1)\times 3=3x+3y-3z=-3$

Now, add the following equations:

$3x+3y-3z=-3\\4x-3y+2z=16$

This gives,

$(3x+4x)+(-3z+2z)=-3+16\\7x-z=13$

We got another new equation as $7x-z=13$ ------- 6

Now, we multiply equation 6 by -5, we get

$(7x-z=13)\times -5=-35x+5z=-65$

Now, we add the above equation and equation 5:

$-35x+5z=-65\\4x-5z=3$

$(-35x+4x)=-65+3\\-31x=-62\\x=\frac{-62}{-31}=2$

Now, we plug in $x=2$ in equation 6, we get

$7\times 2-z=13\\14-z=13\\z=14-13=1$

Now, we plug in $x=2,z=1$ in equation 1, we get

$2+y-1=-1\\1+y=-1\\y=-1-1=-2$

Therefore, $x=2,y=-2,z=1$

The point is $(2,-2,1)$