What is the solution to the system of equations: \( 2x + 3y = 6 \) and \( 4x - y = 5 \)?

To find the solution to the system of equations (2x + 3y = 6) and (4x - y = 5), we can solve it using the method of substitution or elimination.

First, let's express (y) from the first equation. Rearranging (2x + 3y = 6) gives:

[3y = 6 - 2x]

Dividing everything by 3:

[y = 2 - \frac{2}{3}x]

Next, we substitute this expression for (y) into the second equation (4x - y = 5). Substituting gives:

[4x - \left(2 - \frac{2}{3}x\right) = 5]

This simplifies to:

[4x - 2 + \frac{2}{3}x = 5]

Combining like terms, we convert (4x) to a fraction:

(\frac{12}{3}x - 2 + \frac{2}{3}x = 5)

Adding the fractions results in:

[\left(\frac{12 + 2}{3}\