To solve the system of equations:

x + y = 6 \tag{1} 2x - 3y = 4 \tag{2}

we can use the method of substitution or elimination. Here, we'll use the substitution method.

First, solve equation (1) for $x$:

$x = 6 - y$

Next, substitute $x$ from this expression into equation (2):

$2(6 - y) - 3y = 4$

Simplify and solve for $y$:

$12 - 2y - 3y = 4$ $12 - 5y = 4$ $-5y = 4 - 12$ $-5y = -8$ $y = \frac{-8}{-5}$ $y = \frac{8}{5}$ $y = 1.6$

Now, substitute $y = 1.6$ back into the expression $x = 6 - y$ to find $x$:

$x = 6 - 1.6$ $x = 4.4$

So, the solution to the system of equations is:

$x = 4.4$ $y = 1.6$

Would you like more details on this solution or have any questions?

Here are 5 more questions you might ask:

1. How do you solve a quadratic equation?
2. What is the derivative of $f(x) = x^3 + 3x^2 + 5x + 7$?
3. How do you find the area under a curve using integration?
4. Can you explain the Pythagorean theorem?
5. How do you simplify complex fractions?

Tip: When solving systems of linear equations, always check your solution by substituting the values back into the original equations to verify correctness.