# How do I solve a four variable simultaneous equations congruent modulo n? [closed]

I have a set of 4 equations $$\begin{cases} a_1x+b_1y+c_1z+d_1w \equiv P \mod n \\ a_2x+b_2y+c_2z+d_2w \equiv Q \mod n \\ a_3x+b_3y+c_3z+d_3w \equiv R \mod n \\ a_4x+b_4y+c_4z+d_4w \equiv S \mod n\\ \end{cases}$$ Looking for help. Thanks in advance

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• Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please edit the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. Commented Jun 11 at 10:35
• solve them the same way you would solve an ordinary system for example with Cramer rules under the condition that the determinant of the system is not $0 \color{red}{ \ (\mod n)}$... Commented Jun 11 at 12:27