Question

solve the system of equations
8x-6y=48
8x+6y=48

Answer 1

To solve the system of equations:

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

We can solve this system using the elimination method or substitution. Here, we will use the elimination method.

First, let's add both equations together:

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

This simplifies to:

\[
16x = 96
\]

Next, we can solve for \( x \):

\[
x = \frac{96}{16} = 6
\]

Now that we have \( x = 6 \), we can substitute this value back into either of the original equations to find \( y \). We'll use Equation 1:

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

This simplifies to:

\[
48 - 6y = 48
\]

Subtracting 48 from both sides gives:

\[
-6y = 0
\]

Dividing both sides by -6:

\[
y = 0
\]

So the solution to the system of equations is:

\[
x = 6,\, y = 0
\]

Thus, the solution is \((6, 0)\).