Question

y=8x-16
3x-2y=6
substitution

Answer 1

To solve the system of equations using the substitution method, we'll start with the two equations provided:

1. \( y = 8x - 16 \)
2. \( 3x - 2y = 6 \)

Since the first equation is already solved for \( y \), we can substitute it into the second equation.

### Step 1: Substitute \( y \) in the second equation
Now, we substitute \( y \) from the first equation into the second equation:

\[
3x - 2(8x - 16) = 6
\]

### Step 2: Simplify the equation
Now, distribute the -2 in the equation:

\[
3x - 16x + 32 = 6
\]

Combine like terms:

\[
-13x + 32 = 6
\]

### Step 3: Solve for \( x \)
Subtract 32 from both sides:

\[
-13x = 6 - 32
\]

\[
-13x = -26
\]

Now divide by -13:

\[
x = 2
\]

### Step 4: Solve for \( y \)
Now that we have \( x \), we can substitute it back into the first equation to find \( y \):

\[
y = 8(2) - 16
\]

\[
y = 16 - 16
\]

\[
y = 0
\]

### Conclusion
The solution to the system of equations is:

\[
(x, y) = (2, 0)
\]

You can check this by substituting \( x = 2 \) and \( y = 0 \) back into both original equations to ensure they hold true.