The problem asks us to solve a system of two linear equations by graphing. The system of equations is: $3x - 5y = 15$ $6x + y = -3$ We need to determine the solution, if it exists, or state if there are infinitely many solutions or no solution.

1. Problem Description

The problem asks us to solve a system of two linear equations by graphing. The system of equations is:

$3x - 5y = 15$

$6x + y = -3$

We need to determine the solution, if it exists, or state if there are infinitely many solutions or no solution.

2. Solution Steps

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

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, $6x + y = -3$:

$y = -6x - 3$

The slope of the first equation is $\frac{3}{5}$ and the y-intercept is $-3$.

The slope of the second equation is $-6$ and the y-intercept is $-3$.

Since the slopes are different and the y-intercept is the same, the lines intersect at a single point, which is the y-intercept. The y-intercept occurs when $x = 0$.

Plugging in $x=0$ to both equations:

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

$y = -6(0) - 3 = -3$

So the intersection point is $(0, -3)$.

3. Final Answer

The solution to the system is $(0, -3)$.