Let's work through the system of equations presented in your image by eliminating the fractions.

The system of equations is:

$\frac{5x}{2} + \frac{5y}{3} = \frac{95}{6}$ $\frac{x}{4} + \frac{y}{3} = \frac{23}{12}$

Step 1: Eliminate fractions in the first equation

The least common denominator (LCD) for $2$, $3$, and $6$ is $6$. Multiply every term in the first equation by 6:

$6 \times \left( \frac{5x}{2} \right) + 6 \times \left( \frac{5y}{3} \right) = 6 \times \frac{95}{6}$

This simplifies to:

$3(5x) + 2(5y) = 95$

$15x + 10y = 95$

Step 2: Eliminate fractions in the second equation

The least common denominator for $4$, $3$, and $12$ is $12$. Multiply every term in the second equation by 12:

$12 \times \left( \frac{x}{4} \right) + 12 \times \left( \frac{y}{3} \right) = 12 \times \frac{23}{12}$

This simplifies to:

$3x + 4y = 23$

Step 3: Solve the system of equations

We now have the system of equations:

1. $15x + 10y = 95$
2. $3x + 4y = 23$

Let's solve this system using substitution or elimination. I'll use the elimination method.

Multiply the second equation by 5 to align the $x$ terms with the first equation:

$5(3x + 4y = 23) \implies 15x + 20y = 115$

Now subtract the first equation from this result:

$(15x + 20y) - (15x + 10y) = 115 - 95$

Simplifying:

$10y = 20$

$y = 2$

Step 4: Substitute $y = 2$ into one of the original equations

Substitute $y = 2$ into $3x + 4y = 23$:

$3x + 4(2) = 23$

$3x + 8 = 23$

$3x = 15$

$x = 5$

Final Answer:

The solution to the system is $x = 5$ and $y = 2$. The ordered pair is $(5, 2)$.

So, the correct choice is A: The solution is $(5, 2)$.

Would you like further details or have any questions? Here are five additional questions that might be helpful for related learning:

1. How can we check the solution to ensure it's correct?
2. What is the elimination method and how does it compare to substitution?
3. Could this system have had infinitely many solutions? How can we tell?
4. Why do we use the least common denominator when eliminating fractions?
5. How do the values of $x$ and $y$ change if the equations were altered?

Tip: Always check your solution by substituting the values back into the original equations!