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To solve the system of linear equations using matrices, we can rewrite the given equations in matrix form. The provided system is:

\[
\frac{x - 3y}{2} = 0 \quad \text{and} \quad 2x + y = 7
\]

First, we rewrite the first equation to eliminate the fraction:

\[
x - 3y = 0
\]

Now, we have the system:

\[
\begin{cases}
x - 3y = 0 \\
2x + y = 7
\end{cases}
\]

Next, we express this system in matrix form \(AX = B\):

\[
\begin{pmatrix}
1 & -3 \\
2 & 1
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
0 \\
7
\end{pmatrix}
\]

Here, the matrix \(A\) is the coefficients matrix, \(X\) is the variables matrix, and \(B\) is the constants matrix. We need to solve for \(X\) using the equation \(X = A^{-1}B\).

1. Calculate the determinant of \(A\):

\[
\text{det}(A) = (1)(1) - (-3)(2) = 1 + 6 = 7
\]

Since the determinant is non-zero, \(A\) is invertible.

2. Find the inverse of \(A\):

\[
A^{-1} = \frac{1}{\text{det}(A)}
\begin{pmatrix}
1 & 3 \\


Learn how to solve a system of linear equations using matrices with a step-by-step solution. This problem involves converting linear equations into matrix form, calculating determinants, and using matrix inversion to find the solution. Suitable for students in Grades 10-12.

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