To solve the system of equations:

1. $2x + 3y = 19$
2. $4x - 5y = 5$

We can use the method of elimination or substitution. Here, I'll use the elimination method:

1. Multiply the first equation by 2 to align the coefficients of $x$:

$4x + 6y = 38$

2. Now we have the modified system:

$4x + 6y = 38 \quad \text{(Equation 3)}$ $4x - 5y = 5 \quad \text{(Equation 2)}$

3. Subtract Equation 2 from Equation 3:

$(4x + 6y) - (4x - 5y) = 38 - 5$

$4x + 6y - 4x + 5y = 33$

$11y = 33$

$y = \frac{33}{11} = 3$

4. Substitute $y = 3$ back into the first original equation to solve for $x$:

$2x + 3(3) = 19$

$2x + 9 = 19$

$2x = 19 - 9$

$2x = 10$

$x = \frac{10}{2} = 5$

Thus, the solution to the system of equations is:

$x = 5, \quad y = 3$

Would you like details or have any questions?

Here are 5 more math-related questions you might be interested in:

1. How do you solve a quadratic equation using the quadratic formula?
2. Can you explain the Pythagorean theorem with an example?
3. How do you find the derivative of a function using the power rule?
4. What is the process for solving a system of linear equations using matrix methods?
5. How do you integrate a function using substitution?

Tip: When solving systems of equations, aligning coefficients for elimination can simplify the process of finding the solution.