Question

solve the system by substitution.
$y = 5x$
$y = 7x - 16$

Explanation:

Step1: Substitute \( y = 5x \) into \( y = 7x - 16 \)

Since both equations equal \( y \), we can set them equal to each other: \( 5x = 7x - 16 \)

Step2: Solve for \( x \)

Subtract \( 7x \) from both sides: \( 5x - 7x = -16 \) which simplifies to \( -2x = -16 \). Then divide both sides by \( -2 \): \( x = \frac{-16}{-2} = 8 \)

Step3: Find \( y \) using \( y = 5x \)

Substitute \( x = 8 \) into \( y = 5x \): \( y = 5\times8 = 40 \)

Answer:

The solution to the system is \( x = 8 \), \( y = 40 \) or the ordered pair \( (8, 40) \)