The problem is to solve the following system of linear equations: $\frac{2}{3}x - y = 2$ $3x - \frac{3}{4}y = 24$

1. Problem Description

The problem is to solve the following system of linear equations:

$\frac{2}{3}x - y = 2$

$3x - \frac{3}{4}y = 24$

2. Solution Steps

First, let's rewrite the equations:

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

Equation (2): $3x - \frac{3}{4}y = 24$

Multiply equation (1) by $-\frac{3}{4}$:

$-\frac{3}{4} * (\frac{2}{3}x - y) = -\frac{3}{4} * 2$

$-\frac{1}{2}x + \frac{3}{4}y = -\frac{3}{2}$

Now we have the following system:

$-\frac{1}{2}x + \frac{3}{4}y = -\frac{3}{2}$

$3x - \frac{3}{4}y = 24$

Add the two equations:

$(3x - \frac{1}{2}x) + (\frac{3}{4}y - \frac{3}{4}y) = 24 - \frac{3}{2}$

$\frac{5}{2}x = \frac{48}{2} - \frac{3}{2}$

$\frac{5}{2}x = \frac{45}{2}$

$x = \frac{45}{2} * \frac{2}{5}$

$x = 9$

Substitute $x = 9$ into equation (1):

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

$6 - y = 2$

$y = 6 - 2$

$y = 4$

So the solution is $(x, y) = (9, 4)$.

3. Final Answer

The solution to the system is (9, 4).