The image contains a system of linear equations, and the task is to find the values of $a$ and $b$ for which $x = a$ and $y = b$, and then calculate $a - 3b$.

The system of equations is:

$\frac{3}{4}x - \frac{1}{3}y = 5$ $\frac{1}{2}x + \frac{2}{3}y = -2$

Steps to Solve:

1. Multiply both equations by suitable factors to eliminate fractions.
2. Solve the system using either substitution or elimination to find $x = a$ and $y = b$.
3. Calculate $a - 3b$.

Let's begin by solving this system of equations.

Equation 1:

$\frac{3}{4}x - \frac{1}{3}y = 5$ Multiplying through by 12 to eliminate denominators: $12 \times \frac{3}{4}x - 12 \times \frac{1}{3}y = 12 \times 5$ This simplifies to: $9x - 4y = 60$ (Equation A)

Equation 2:

$\frac{1}{2}x + \frac{2}{3}y = -2$ Multiplying through by 6 to eliminate denominators: $6 \times \frac{1}{2}x + 6 \times \frac{2}{3}y = 6 \times -2$ This simplifies to: $3x + 4y = -12$ (Equation B)

Now let's solve these two equations:

1. $9x - 4y = 60$
2. $3x + 4y = -12$

We can add the two equations to eliminate $y$.

I'll solve this next.The solution to the system of equations is:

$x = 4 \quad \text{and} \quad y = -6$

Thus, $a = 4$ and $b = -6$.

Now, let's calculate $a - 3b$:

$a - 3b = 4 - 3(-6) = 4 + 18 = 22$

So, the value of $a - 3b$ is 22.

Would you like more details or have any questions? Here are five related problems to practice:

1. Solve the system of equations: $\frac{2}{3}x + \frac{1}{4}y = 7$ and $\frac{5}{6}x - \frac{1}{3}y = 2$.
2. Find the value of $2a + 5b$ given that $x = a$ and $y = b$ for the system: $\frac{1}{5}x + \frac{2}{7}y = 4$ and $\frac{3}{5}x - \frac{1}{7}y = -3$.
3. What is the value of $a + b$ when $\frac{1}{3}x - \frac{1}{2}y = 8$ and $\frac{5}{6}x + \frac{3}{4}y = -5$?
4. If $x = 7$ and $y = -4$, what is the value of $2x - 3y$?
5. Solve $4x + 2y = 10$ and $3x - 4y = 5$ for $x$ and $y$.

Tip: When solving systems of linear equations, multiplying to eliminate fractions can simplify the process significantly.