Question 804413
Equation A:{{{2x-y+z=7}}}
Equation B:{{{x+2y+2z=3}}}
Equation C:{{{7x-3y-3z=4}}}
For these kind of problems, you need to start by eliminating either x, y, or z.
We are going to start with x.
Take 2 of the 3 given equations.
I am going to use Equation A and B.
{{{2x-y+z=7}}}
{{{x+2y+2z=3}}}
you want the x's to be opposites.
To do so we are going to multiply equation B by -2.
{{{-2(x+2y+2z)=-2(3)}}}
{{{-2x-4y-4z=-6}}}
now you add the two equations together.
{{{2x-y+z=7}}}
+
{{{-2x-4y-4z=-6}}}
{{{-5y-3z=1}}}
Now lets take equation B and C and eliminate x again.
{{{x+2y+2z=3}}}
{{{7x-3y-3z=4}}}
we will multiply equation B by -7.
{{{-7(x+2y+2z)=-7(3)}}}
{{{-7x-14y-14z-21}}}
add the two equations together
{{{-7x-14y-14z-21}}}
+
{{{7x-3y-3z=4}}}
{{{-17y-17z=-17}}}
you can divide the equation by-17
{{{(-17y-17z)/-17=-17/-17}}}
{{{y+z=1}}}
We now have two equations with only y and z. 
{{{-5y-3z=1}}}
{{{y+z=1}}}
We will now eliminate z
multiply {{{y+z=1}}} by 3
{{{3y+3z=3}}}
add the two equations.
{{{-5y-3z=1}}}
+
{{{3y+3z=3}}}
{{{-2y=4}}}
{{{y=-2}}}
plug y=-2 into {{{y+z=1}}}
{{{-2+z=1}}}
{{{z=3}}}
Now plug y=-2 and z=3 into equation A.
{{{2x-2+3=7}}}
{{{2x=6}}}
{{{x=3}}}
the answer is x=3, y=-2, and z=3.