Sure! Let's solve the given system of equations step-by-step.
We are given the following system:
[tex]\[
\begin{array}{r}
4x - y = 3 \\
6x - 2y = 2
\end{array}
\][/tex]
To find the solution, we can use matrix methods. Here's how we do it:
1. Write the system in matrix form:
[tex]\[
A \cdot \mathbf{x} = \mathbf{B}
\][/tex]
where [tex]\(A\)[/tex] is the coefficient matrix, [tex]\(\mathbf{x}\)[/tex] is the variable matrix, and [tex]\(\mathbf{B}\)[/tex] is the constant matrix.
[tex]\[
A = \begin{pmatrix}
4 & -1 \\
6 & -2
\end{pmatrix}, \quad
\mathbf{x} = \begin{pmatrix}
x \\
y
\end{pmatrix}, \quad
\mathbf{B} = \begin{pmatrix}
3 \\
2
\end{pmatrix}
\][/tex]
2. Solve the matrix equation [tex]\(A \cdot \mathbf{x} = \mathbf{B}\)[/tex]:
When we solve for [tex]\(\mathbf{x}\)[/tex], we get:
[tex]\[
\begin{pmatrix}
x \\
y
\end{pmatrix} =
\begin{pmatrix}
2 \\
5
\end{pmatrix}
\][/tex]
Thus, the solution to the system of equations is:
[tex]\[
x = 2, \, y = 5
\][/tex]
So, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
