We are asked to solve the system of linear equations by graphing: $5x - 4y = 20$ $6x + y = -5$

1. Problem Description

We are asked to solve the system of linear equations by graphing:

$5x - 4y = 20$

$6x + y = -5$

2. Solution Steps

First, we rewrite each equation in slope-intercept form ($y = mx + b$).

For the first equation, $5x - 4y = 20$, we solve for $y$:

$-4y = -5x + 20$

$y = \frac{-5x + 20}{-4}$

$y = \frac{5}{4}x - 5$

For the second equation, $6x + y = -5$, we solve for $y$:

$y = -6x - 5$

Now, we find the point of intersection by setting the two equations equal to each other:

$\frac{5}{4}x - 5 = -6x - 5$

$\frac{5}{4}x + 6x = 0$

$\frac{5}{4}x + \frac{24}{4}x = 0$

$\frac{29}{4}x = 0$

$x = 0$

Now, substitute $x = 0$ into either equation to find $y$. Using the second equation:

$y = -6(0) - 5$

$y = -5$

Therefore, the solution to the system of equations is $(0, -5)$.

3. Final Answer

The solution is $(0, -5)$.