SOLUTION: Can you pretty please with a cherry on top help me with this. Im terribly confused. Thank you (: 2x - y + z = 7 x + 2y + 2z = 3 7x - 3y - 3z = 4

Algebra ->  Matrices-and-determiminant -> SOLUTION: Can you pretty please with a cherry on top help me with this. Im terribly confused. Thank you (: 2x - y + z = 7 x + 2y + 2z = 3 7x - 3y - 3z = 4      Log On


   

Question 804413: Can you pretty please with a cherry on top help me with this. Im terribly confused. Thank you (:
2x - y + z = 7
x + 2y + 2z = 3
7x - 3y - 3z = 4
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
Equation A:2x-y%2Bz=7
Equation B:x%2B2y%2B2z=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%2Bz=7
x%2B2y%2B2z=3
you want the x's to be opposites.
To do so we are going to multiply equation B by -2.
-2%28x%2B2y%2B2z%29=-2%283%29
-2x-4y-4z=-6
now you add the two equations together.
2x-y%2Bz=7
+
-2x-4y-4z=-6
-5y-3z=1
Now lets take equation B and C and eliminate x again.
x%2B2y%2B2z=3
7x-3y-3z=4
we will multiply equation B by -7.
-7%28x%2B2y%2B2z%29=-7%283%29
-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
%28-17y-17z%29%2F-17=-17%2F-17
y%2Bz=1
We now have two equations with only y and z.
-5y-3z=1
y%2Bz=1
We will now eliminate z
multiply y%2Bz=1 by 3
3y%2B3z=3
add the two equations.
-5y-3z=1
+
3y%2B3z=3
-2y=4
y=-2
plug y=-2 into y%2Bz=1
-2%2Bz=1
z=3
Now plug y=-2 and z=3 into equation A.
2x-2%2B3=7
2x=6
x=3
the answer is x=3, y=-2, and z=3.