The problem asks us to solve the following system of linear equations by graphing: $3x - 5y = 15$ $6x + y = -3$

1. Problem Description

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

$3x - 5y = 15$

$6x + y = -3$

2. Solution Steps

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

Equation 1: $3x - 5y = 15$

Subtract $3x$ from both sides:

$-5y = -3x + 15$

Divide both sides by $-5$:

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

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

Equation 2: $6x + y = -3$

Subtract $6x$ from both sides:

$y = -6x - 3$

Now we have both equations in slope-intercept form:

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

$y = -6x - 3$

From equation 1 ($y = \frac{3}{5}x - 3$), the slope is $\frac{3}{5}$ and the y-intercept is $-3$.

From equation 2 ($y = -6x - 3$), the slope is $-6$ and the y-intercept is $-3$.

Since both equations have the same y-intercept ($-3$), the lines intersect at the point where $x=0$ and $y=-3$.

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

3. Final Answer

$(0, -3)$