Solve the System of Equations: x - y = 8 and 3x + 2y = 24

To solve this problem, we'll follow these steps:

• Step 1: Solve the first equation for one variable
• Step 2: Substitute into the second equation
• Step 3: Solve for the second variable
• Step 4: Use this value to find the first variable

Now, let's work through each step:
Step 1: From the equation $x - y = 8$, solve for $x$:

$x = y + 8$

Step 2: Substitute $x = y + 8$ into the second equation $3x + 2y = 24$.

$3(y + 8) + 2y = 24$

Simplify:
$3y + 24 + 2y = 24$

Combine like terms:
$5y + 24 = 24$

Step 3: Solve for $y$:

$5y = 24 - 24$

$5y = 0$

$y = 0$

Step 4: Substitute $y = 0$ back into the expression for $x$:

$x = 0 + 8$

$x = 8$

Therefore, the solution to the system of equations is $x = 8$ and $y = 0$.

This matches choice 1.