The problem asks us to solve the following system of equations by graphing: $5x + y = 8$ $3x - y = 8$

1. Problem Description

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

$5x + y = 8$

$3x - y = 8$

2. Solution Steps

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

For the first equation, $5x + y = 8$, we subtract $5x$ from both sides to get:

$y = -5x + 8$

The slope is $-5$ and the y-intercept is $8$.

For the second equation, $3x - y = 8$, we subtract $3x$ from both sides to get:

$-y = -3x + 8$

Multiply both sides by $-1$ to get:

$y = 3x - 8$

The slope is $3$ and the y-intercept is $-8$.

Now we find the intersection point of the two lines. We can set the two expressions for $y$ equal to each other:

$-5x + 8 = 3x - 8$

Add $5x$ to both sides:

$8 = 8x - 8$

Add $8$ to both sides:

$16 = 8x$

Divide both sides by $8$:

$x = 2$

Now substitute $x = 2$ into either equation to find $y$. Using the first equation $y = -5x + 8$:

$y = -5(2) + 8 = -10 + 8 = -2$

So the intersection point is $(2, -2)$.

3. Final Answer

The solution to the system of equations is $(2, -2)$.