We are asked to solve the given system of equations by graphing and check the solution. The system of equations is: $5x + y = 8$ $3x - y = 8$

1. Problem Description

We are asked to solve the given system of equations by graphing and check the solution. The system of equations is:

$5x + y = 8$

$3x - y = 8$

2. Solution Steps

First, we will solve each equation for $y$.

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

$y = 8 - 5x$

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

$-y = 8 - 3x$

Multiply both sides by $-1$ to get:

$y = 3x - 8$

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

$y = -5x + 8$

$y = 3x - 8$

To find the intersection point, which is the solution to the system, we set the two equations equal to each other:

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

Add $5x$ to both sides:

$8 = 8x - 8$

Add $8$ to both sides:

$16 = 8x$

Divide by $8$:

$x = 2$

Now substitute $x = 2$ into either equation to find the value of $y$. Let's use the second equation:

$y = 3(2) - 8$

$y = 6 - 8$

$y = -2$

So the solution is $x = 2$ and $y = -2$. We can write this as the ordered pair $(2, -2)$.

We can check our solution by plugging the values into the original equations:

$5x + y = 8$

$5(2) + (-2) = 10 - 2 = 8$. This is correct.

$3x - y = 8$

$3(2) - (-2) = 6 + 2 = 8$. This is correct.

3. Final Answer

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