X= Y= Z= I need one example and then I have it?

Question

3x + 2y + 2z = 19
2x - 1y - 3z = -2
-13x - 4y + 0z = -56

X=
Y=
Z=

Thank you :)

Answer 1

3x + 2y + 2z = 19- - - - - Equation 1
2x - y - 2z = - 2- - - - -- -Equation 2
- 13x - 4y + 0z = - 56- - -Equation 3
- - - - - - - - - - - - - -

Multiply equation 1 by 3 and equation 2 by 2

3x + 3y + 2z = 19

3(3x) + 3(2y) +3(2z) =3(19)

9x + 6y + 6z = 38
- - - - - - -

2x - y - 3z = - 2

2(2x) - 2y) - 2(3z) = - 2(2)

4x - 2y - 6z = - 4
- - - - - - --

Elimination of z

9x + 6y + 6z = 38
4x - 2y - 6z = - 4
- - - - - - -

13x + 4y = 34. . .Equation 4

- - - - - -- - - -

On equation 3

-13x - 4y + 0z - 56

The 0z = 0

- - - - - - - -

13x + 4y = 34
-13x - 4y = - 56
- - - - - - - - -
0 + 0 = - 22

The x and y coefficient and variable cancell. There is no solution for this problem.

- - - - - - - -s-

Answer 2

Take one of the equations and solve for z in terms of x and y. Then take the value for z and sub it into one of the other equations; solve that equation for y in terms of x. Take the values for z and y and sub them into the third equation; solve that equation for x. With the value of x, you can solve for y (which was known in terms of x) and then for z (which was known in terms of x and y). You could actually deal with the variables in any order.

I'd start by solving for y in terms of x by using the third equation. -13x - 4y = -56 ==> 4y = 13x + 56 ==> y = (13/4)x + 14. Then I'd solve for z in the second equation. 2x - y - 3z = -2 ==> 2x - ((13/4)x + 14) - 3z = -2 ==> 2x - (13/4)x - 14 - 3z = -2 ==> (-5/4)x - 3z = 12 ==> 3z = (-5/4)x - 12 ==> z = (-5/12)x - 4. Finally, you can take your values for y and z in terms of x and sub them into the first equation, which you can then solve algebraically for x. After that, plug the value of x into the expressions for y and z to solve for them.

Answer 3

You need to remove variables. The last one is perfect because it's already got no Z. So solve that for y (y = (-56+13x)/4) and plug that nasty thing back into the last equation in place of y and now you have a single variable to solve for. Once you have solved for x, you can use the same technique to solve for the others.

Messy, but it will work.

Answer 4

X=4
Y=1
Z=3

This formula only works for the last two, I hope I was a little bit of help.
You're welcome :)

Answer 5

3x+2X-13X=5x-13x=-8x
2y-y-4y=2y-5y=-3y
2z-3z=-z

Answer 6

x=4
y=-3
z=-43