Question

how many solutions does the system of equations have? 8x - 6y = 48
8x + 6y = 48

Answer 1

To determine how many solutions the system of equations has, we can analyze the two equations:

1. \( 8x - 6y = 48 \)
2. \( 8x + 6y = 48 \)

We can solve this system by either substitution or elimination. Here, we'll use elimination.

First, let's rewrite both equations for clarity:
- Equation 1: \( 8x - 6y = 48 \)
- Equation 2: \( 8x + 6y = 48 \)

Now, we can subtract Equation 1 from Equation 2:

\[
(8x + 6y) - (8x - 6y) = 48 - 48
\]

This simplifies to:
\[
12y = 0
\]

Solving for \( y \) gives:
\[
y = 0
\]

Now, we can substitute \( y = 0 \) back into either of the original equations to find \( x \). We'll use Equation 1:

\[
8x - 6(0) = 48
\]

This simplifies to:
\[
8x = 48
\]

Dividing both sides by 8 gives:
\[
x = 6
\]

So we have found a single solution: \( (x, y) = (6, 0) \).

To summarize, the system of equations has exactly **one solution**.