Question

solve the system by substitution.

$y = 4x - 8$
$y = 2x$

Explanation:

Step1: Substitute \( y = 2x \) into \( y = 4x - 8 \)

Since both equations are solved for \( y \), we can substitute \( 2x \) for \( y \) in the first equation. So we get \( 2x = 4x - 8 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 2x - 4x = 4x - 8 - 4x \), which simplifies to \( -2x = -8 \). Then divide both sides by \( -2 \): \( \frac{-2x}{-2}=\frac{-8}{-2} \), so \( x = 4 \).

Step3: Substitute \( x = 4 \) into \( y = 2x \)

Now that we have \( x = 4 \), we substitute it into the equation \( y = 2x \). So \( y = 2\times4 = 8 \).

Answer:

The solution to the system is \( x = 4 \) and \( y = 8 \), or as an ordered pair \( (4, 8) \).