# System of 6 variables and 5 equations with parameters

\begin{align*}x_1 + x_2 &= a\\y_1 + y_2 &= b\\z_1 + z_2 &= c\\x_1 + y_1 + z_1 &= 0\\x_2 &= z_2\end{align*}

Solve for $x_1, x_2, y_1, y_2, z_1, z_2$ in terms of $a, b$ and $c$.

• You will still have one free parameter because you have one too few equations. The usual substitution technique will get you there. What have you tried? Where are you stuck? – Ross Millikan Nov 28 '17 at 15:40

An alternative method, if you are familiar with Linear Algebra courses, is expressing the system via matrices in the form $Ax=b$, where $A$ is the matrix of coefficients of the variables, $x$ the $1\times n$ matrix of $n$ variables and $b$ the $1\times n$ right hand matrix of the equations. After that, you can apply the Gauss Elimination Method to yield your solution.
• @Koy Hi ! As you can observe from the last equation of your system, $x_2 = z_2$, you will have a free parameter because there are one few too much equations. That should not make you confused though, you can proceed with the solutions and let the extra parameter be a parameter ! – Rebellos Nov 28 '17 at 20:51