# How do I solve a system of equations?

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Mark Dillon on 11 Aug 2015
Answered: James Wiken on 13 Aug 2015
I need to solve the following system of equations for x:
• 10w-5x+3x-z = 1
• 4x-4y = 2
• z+7x+9w-5y = 3
• 4w-1x+6y+4w+6w = 4
I tried using the solve command, but I don't think I am understanding how to use it properly

John D'Errico on 12 Aug 2015
Mark Dillon on 12 Aug 2015
if true
% code
solve(['10*w-2*x-z=1','4*x-4*y = 2','z+7*x+9*w-5*y = 3','14*w-x+6*y = 4'],[w,x,y,z]);
end

James Wiken on 13 Aug 2015
It looks like you are not quite using the correct syntax for the solve command. What you will want to do is first define 'w, x, y, z' as 'sym' variables.
syms w x y z
You can then define each equation using the 'sym' notation. For example, your first equation would change from
'10*w-2*x-z=1'
to
10*w-2*x-z == 1
You may want to look at the following documentation page for the 'solve' function:
An example of solving linear equations using the Symbolic Toolbox can also be found here:
You could also solve this system of equations numerically. Because the system of equations you are solving is linear, you can also rewrite the system of equations into matrix form. Refer to the following documentation link for doing this:
This method of solving the system of equations does not require using the Symbolic Toolbox and is generally much faster, especially if your system of equations is large and you do not need symbolic solutions.

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