Question

find the solution set for x, y, z

2x + y - 2z= 3
3x - y - 3z= 2
5x + 6y -2z= 2

Answer 1

Do you know how to use augmented matrices?

Answer 2

You will have to solve for x, y and z separately.
You would start be eliminating 1 unknown from the equations:

A) 2x + y - 2z= 3
B) 3x - y - 3z= 2
C) 5x + 6y -2z= 2

Multiply equation C by minus 1 then add all 3 equations:
A) 2x + y - 2z= 3
B) 3x - y - 3z= 2
C) -5x - 6y +2z= -2

Total of all 3 = -6y -3z = 3
-3z = 6y +3
-z = 2y + 1
or z = -2y -1
inputting this value of z into equation A and B
A) 2x + y - 2z= 3
B) 3x - y - 3z= 2

2x + y + 4y +2 = 3
3x -y + 6y + 3 = 2

Multiplying equation B by -2/3
-2x + (2/3)y -4y -2 = -4/3 then adding equation A
2x + y + 4y +2 = 3 sums to

(5/3)y = (5/3)
Y = 1
We have solved the first unknown

Answer 3

Can you solve for x and z?

Answer 4

Oh wow, you didn't hold back wolf man

Answer 5

Thanks snowfire

Answer 6

@Snowfire
\(\left[\begin{array}{ccc|c}
2 & 1 &- 2& 3 \\
3 & -1& - 3& 2 \\
5 & 6 & -2 & 2
\end{array}\right]

\)

Now they just need to put it in rref. \(\large\ddot \smile\)