Systems of 3 equations in three ?

Question

-2x+4y+z=25

x+2y-z=-3

3x-3y+2z=-11

2x+y-3z=-7

x-2y-z=4

3x+4y+z=2

I know the solutions, but I run into difficulties when trying to solve them!

Thanks in advance!

Answer 1

I'll do one.

2x+y-3z=-7

x-2y-z=4

3x+4y+z=2

Multiply the first equation by 2, and add it to the second: 5x -7z = -10

Multiply the first equation by -4, and add it to the third: -5x +13z = 30

Now add these two new equations.

5x -7z = -10

-5x +13z = 30

------------------------

6z = 20

z = 20/6 = 10/3

Then go back to find x.

5x - 7(10/3) = -10

5x - 70/3 = -30/3

5x = 40/3

x = 8/3

Then go back to find y.

2(8/3) + y - 3(10/3) = -7

16/3 + y - 30/3 = -7

-14/3 + y = -21/3

y = -7/3

Answer: (8/3, -7/3, 10/3)

Check to see that this works in the other two equations.