The problem is to solve the system of inequalities: $5x + y > 6$ $x - 2y > 7$

1. Problem Description

The problem is to solve the system of inequalities:

$5x + y > 6$

$x - 2y > 7$

2. Solution Steps

We need to solve the system of inequalities.

First, let's isolate $y$ in both inequalities.

For the first inequality, $5x + y > 6$, we subtract $5x$ from both sides:

$y > -5x + 6$

For the second inequality, $x - 2y > 7$, we subtract $x$ from both sides:

$-2y > -x + 7$

Now, divide by $-2$. Remember to flip the inequality sign when dividing by a negative number:

$y < \frac{1}{2}x - \frac{7}{2}$

Now we have the two inequalities in slope-intercept form:

$y > -5x + 6$

$y < \frac{1}{2}x - \frac{7}{2}$

We cannot give a numerical solution for $x$ and $y$, but rather describe the region where both inequalities hold true. The solution set consists of all points $(x, y)$ that satisfy both inequalities.

3. Final Answer

The solution to the system of inequalities is given by:

$y > -5x + 6$

$y < \frac{1}{2}x - \frac{7}{2}$

The solution is the region where both these inequalities are satisfied.