[Math] How to solve a system of 3 equations with Cramer’s Rule

Question

I am given the following system of 3 simultaneous equations:

$$
\begin{align*}
4a+c &= 4\\
19a + b – 3c &= 3\\
7a + b &= 1\end{align*}
$$

How do I solve using Cramers' rule?

For one, I do know that by putting as a matrix the LHS
$$\begin{pmatrix}
4&0&1\\19&1&-3\\7&1&0
\end{pmatrix}$$

and then computing its determinant to be $24$ is of some use…but could somebody give more ideas?

Answer 1

In the below tutorial, they mention a very easy method to understand Cramer's rule and simplification of 2 as well as 3 equation systems. See the step by step tutorial with a solved example:

Check it here: Cramer’s Rule | 2 & 3 Equation Systems. Easy & Step by Step