The problem asks us to solve the following system of equations by graphing: $5x - 4y = 20$ $6x + y = -5$

1. Problem Description

The problem asks us to solve the following system of equations by graphing:

$5x - 4y = 20$

$6x + y = -5$

2. Solution Steps

First, rewrite both equations in slope-intercept form ($y = mx + b$).

Equation 1: $5x - 4y = 20$

Subtract $5x$ from both sides: $-4y = -5x + 20$

Divide both sides by $-4$: $y = \frac{5}{4}x - 5$

Equation 2: $6x + y = -5$

Subtract $6x$ from both sides: $y = -6x - 5$

Now, we can graph these two equations. The intersection point of the two lines will be the solution to the system of equations.

Looking at the equations, we can guess some points on the graph for both equations.

For equation 1, $y = \frac{5}{4}x - 5$:

If $x = 0$, $y = -5$. So, the point $(0, -5)$ is on the line.

If $x = 4$, $y = \frac{5}{4}(4) - 5 = 5 - 5 = 0$. So, the point $(4, 0)$ is on the line.

For equation 2, $y = -6x - 5$:

If $x = 0$, $y = -5$. So, the point $(0, -5)$ is on the line.

If $x = -1$, $y = -6(-1) - 5 = 6 - 5 = 1$. So, the point $(-1, 1)$ is on the line.

Since both lines pass through $(0, -5)$, the solution to the system of equations is $(0, -5)$.

We can verify this by substituting $x = 0$ and $y = -5$ into the original equations:

$5(0) - 4(-5) = 0 + 20 = 20$. This is correct.

$6(0) + (-5) = 0 - 5 = -5$. This is correct.

3. Final Answer

(0, -5)