We are asked to solve the following system of equations by graphing: $5x - 3y = 15$ $2x + y = -5$

1. Problem Description

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

$5x - 3y = 15$

$2x + y = -5$

2. Solution Steps

First, let's 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, $5x - 3y = 15$, we can solve for $y$:

$-3y = -5x + 15$

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

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

For the second equation, $2x + y = -5$, we can solve for $y$:

$y = -2x - 5$

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

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

$y = -2x - 5$

To find the solution graphically, we look for the point where the two lines intersect. Since both equations are equal to y, we can set them equal to each other:

$\frac{5}{3}x - 5 = -2x - 5$

$\frac{5}{3}x + 2x = 0$

$\frac{5}{3}x + \frac{6}{3}x = 0$

$\frac{11}{3}x = 0$

$x = 0$

Now, substitute $x = 0$ into either equation to find the value of $y$. Let's use the second equation:

$y = -2(0) - 5$

$y = -5$

So the solution is the point $(0, -5)$.

We can check the solution by plugging $x=0$ and $y=-5$ into the original equations.

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

$5(0) - 3(-5) = 0 + 15 = 15$, which is true.

For the second equation, $2x + y = -5$:

$2(0) + (-5) = 0 - 5 = -5$, which is true.

3. Final Answer

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