We are asked to solve the following system of equations: $\frac{2}{3}x - y = 1$ (1) $5x - \frac{3}{5}y = 42$ (2) We need to find an ordered pair $(x, y)$ that satisfies both equations, or determine if there are infinitely many solutions or no solution.

1. Problem Description

We are asked to solve the following system of equations:

$\frac{2}{3}x - y = 1$ (1)

$5x - \frac{3}{5}y = 42$ (2)

We need to find an ordered pair $(x, y)$ that satisfies both equations, or determine if there are infinitely many solutions or no solution.

2. Solution Steps

We can use the substitution or elimination method. Let's use the elimination method.

First, multiply equation (1) by $-\frac{3}{5}$ to eliminate $y$:

$-\frac{3}{5} \cdot (\frac{2}{3}x - y) = -\frac{3}{5} \cdot 1$

$-\frac{2}{5}x + \frac{3}{5}y = -\frac{3}{5}$ (3)

Now add equation (2) and equation (3):

$(5x - \frac{3}{5}y) + (-\frac{2}{5}x + \frac{3}{5}y) = 42 + (-\frac{3}{5})$

$5x - \frac{2}{5}x = 42 - \frac{3}{5}$

$\frac{25}{5}x - \frac{2}{5}x = \frac{210}{5} - \frac{3}{5}$

$\frac{23}{5}x = \frac{207}{5}$

$23x = 207$

$x = \frac{207}{23}$

$x = 9$

Now substitute $x = 9$ into equation (1):

$\frac{2}{3}(9) - y = 1$

$6 - y = 1$

$y = 6 - 1$

$y = 5$

The solution is $(9, 5)$. We can check this solution with equation (2):

$5(9) - \frac{3}{5}(5) = 42$

$45 - 3 = 42$

$42 = 42$

The solution satisfies both equations.

3. Final Answer

A. The solution to the system is $(9, 5)$.