The problem is to solve the given system of equations by graphing. The system of equations is: $3x - 5y = 15$ $6x + y = -3$

1. Problem Description

The problem is to solve the given system of equations by graphing. The system of equations is:

$3x - 5y = 15$

$6x + y = -3$

2. Solution Steps

First, we need to rewrite each equation in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

For the first equation, $3x - 5y = 15$:

$-5y = -3x + 15$

$y = \frac{-3x}{-5} + \frac{15}{-5}$

$y = \frac{3}{5}x - 3$

For the second equation, $6x + y = -3$:

$y = -6x - 3$

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

$y = \frac{3}{5}x - 3$

$y = -6x - 3$

To find the solution, we look for the point where the two lines intersect. We can set the two equations equal to each other:

$\frac{3}{5}x - 3 = -6x - 3$

$\frac{3}{5}x + 6x = -3 + 3$

$\frac{3}{5}x + \frac{30}{5}x = 0$

$\frac{33}{5}x = 0$

$x = 0$

Now, substitute $x = 0$ into either equation to find the corresponding $y$ value. Let's use the first equation in slope-intercept form:

$y = \frac{3}{5}(0) - 3$

$y = -3$

Therefore, the solution to the system of equations is $(0, -3)$.

3. Final Answer

The solution is $(0, -3)$.