Please help me!!! solving systems of equations?!?!?!?

Question

3x+y-2z = 10

6x-2y+z = -2

x+4y+3z = 7

Answer 1

use Cramers rule

http://www.maths.surrey.ac.uk/explore/em...

Answer 2

This will take a lot of steps, but each one is straightforward...

Multiply the first equation by 2

6x + 2y - 4z = 20

Add it to the second...

6x + 2y - 4z = 20

6x - 2y +  z = -2

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

12x + 0y - 3z = 18

or

4x - z = 6

z = 4x - 6

Plug this value into the second and third equations...

6x - 2y + (4x - 6) = -2

10x - 2y -6 = -2

10x - 2y = 4

5x - y = 2

and

x + 4y + 3(4x - 6) = 7

x + 4y + 12x - 18 = 7

13x + 4y = 25

This gives you two equations and two unknowns...

5x - y = 2

13x + 4y = 25

Multiply the top by 4, and add

20x - 4y = 8

13x + 4y = 25

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

33x + 0y = 33

33x = 33

x = 1

Plug this back into the bottom...

13 + 4y = 25

4y = 12

y = 3

From above

z = 4x - 6

z = 4 - 6

z = -2

x = 1

y = 3

z = -2

Now, plug these values back into the original equations to check.

3*1 + 2 - 2(-2) = 10

3 + 2  + 4 = 10

10 = 10 CHECK

6 - 2(3) + (-2) = -2

6 - 6 - 2 = -2

-2 = -2 CHECK

1 + 4*3 + 3(-2) = 7

1 + 12 - 6 = 7

7 = 7 CHECK

So,

x = 1

y = 3

z = -2