Solve the system of equations. {y−2=8x2y−4=4x

Answer 1

To solve the system of equations given by

1. \( y - 2 = 8x \)
2. \( 2y - 4 = 4x \)

let's start by simplifying each equation.

Step 1: Simplify the equations

1. From the first equation \( y - 2 = 8x \), we can express \( y \) in terms of \( x \):

   \[ y = 8x + 2 \]

2. From the second equation \( 2y - 4 = 4x \), we can simplify it to find \( y \):

   Adding 4 to both sides gives us:

   \[ 2y = 4x + 4 \]

   Next, divide each term by 2:

   \[ y = 2x + 2 \]

Now, we have two equations in terms of \( y \):

1. \( y = 8x + 2 \)
2. \( y = 2x + 2 \)

Step 2: Set the two expressions for \( y \) equal to each other

Now we can set the two equations for \( y \) equal to each other:

\[ 8x + 2 = 2x + 2 \]

Step 3: Solve for \( x \)

Subtract \( 2x \) from both sides:

\[ 8x - 2x + 2 = 2 \]

This simplifies to:

\[ 6x + 2 = 2 \]

Now, subtract 2 from both sides:

\[ 6x = 0 \]

Dividing both sides by 6 gives:

\[ x = 0 \]

Step 4: Find \( y \) using \( x \)

Now we'll substitute \( x = 0 \) back into one of the equations to find \( y \). We'll use either equation; here we’ll use \( y = 2x + 2 \):

\[ y = 2(0) + 2 = 2 \]

Step 5: Write the solution

Thus, the solution to the system of equations is:

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

Conclusion

The solution to the system of equations is \( \boxed{(0, 2)} \).