We are given a system of two linear equations with two variables, $x$ and $y$: $\frac{x}{2} + \frac{y}{3} = 5$ $2x - y = -1$ We need to find the values of $x$ and $y$ that satisfy both equations.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

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

$2x - y = -1$

We need to find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

First, let's eliminate the fractions in the first equation. Multiply the entire first equation by 6, the least common multiple of 2 and 3:

$6(\frac{x}{2} + \frac{y}{3}) = 6(5)$

$3x + 2y = 30$

Now we have the following system of equations:

$3x + 2y = 30$

$2x - y = -1$

Next, we can solve for $y$ in the second equation:

$y = 2x + 1$

Substitute this expression for $y$ into the first equation:

$3x + 2(2x + 1) = 30$

$3x + 4x + 2 = 30$

$7x + 2 = 30$

$7x = 28$

$x = 4$

Now that we have the value of $x$, we can find the value of $y$ using the equation $y = 2x + 1$:

$y = 2(4) + 1$

$y = 8 + 1$

$y = 9$

3. Final Answer

$x = 4$ and $y = 9$.