SOLUTION: {{{system(-10x - 11y + 7z = 145, 7x - 4y - 3z = 53, -5x - y = 146)}}} I need to solve this using any method. Id like to see the steps and the correct answer. I thi

You can put this solution on YOUR website!
If you know matrices, you can use that. But I suspect you are not there yet.
So, you might try substitution.
I would start with equation 3. Use it to find y in terms of x



You can then substitute that value for y into both equations 1 and 2.


Simplify this to get an equation with just x and z in it
Use it to find x in terms of z


Simplify this one too and get an equation with just x and z.
Substitute the z value in this last equation with the "z in terms of x" from the earlier equation.
You now have one equation with only x and constants in it.
Solve for x.
Niw use this value of x and the equation with z in terms of x to find z.
Then use x and z in any of the equations to solve for y (I would use the third original equation since it has only x and y in it)

You can put this solution on YOUR website!
Edwin's solution:

That would work, but it would be the best way.

First you should observe that z is already eliminated
from the third equation, so you should eliminate z 
from the first two equations:

To eliminate z from the first two equations:

Multiply the first equation by 3 and the second equation 
by 7, then add them:

3[-10x - 11y + 7z = 145]
7[  7x -  4y - 3z =  53]

  -30x - 33y + 21z = 435
   49x - 28y - 21z = 371
   19x - 61y       = 806

Now we take the third original equation with
this equation and solve this system:



We can do this by substitution:

Solve the first equation for y:



Substitute  for  in








Substitute that into 





Now substitute  and  into
either one of the first two original equations.








Edwin