APFIVE Solving a Matrix Vector Equation
Consider the linear transformation represented by the matrix $$\begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$$. If this transformation maps the vector $$\begin{bmatrix} x \\ y \end{bmatrix}$$ to $$\begin{bmatrix} 7 \\ 5 \end{bmatrix}$$, what are the values of $$x$$ and $$y$$?
A
$$x = \frac{19}{7}, y = \frac{4}{7}$$
B
$$x = 1, y = 4$$
C
$$x = 2, y = 3$$
D
$$x = 4, y = 1$$
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