Question

question
solve the system by substitution.

$y = 7x - 45$
$y = 2x$

Explanation:

Step1: Substitute \( y = 2x \) into \( y = 7x - 45 \)

Since both equations equal \( y \), we can set them equal to each other. So substitute \( y \) in the first equation with \( 2x \) from the second equation: \( 2x = 7x - 45 \)

Step2: Solve for \( x \)

Subtract \( 7x \) from both sides: \( 2x - 7x = 7x - 45 - 7x \), which simplifies to \( -5x = -45 \). Then divide both sides by \( -5 \): \( \frac{-5x}{-5} = \frac{-45}{-5} \), so \( x = 9 \)

Step3: Solve for \( y \)

Substitute \( x = 9 \) into \( y = 2x \): \( y = 2\times9 = 18 \)

Answer:

The solution to the system is \( x = 9 \) and \( y = 18 \), or as an ordered pair \( (9, 18) \)