Question

solve the system by substitution.

$y = -2x + 28$

$y = 5x$

Explanation:

Step1: Substitute \( y = 5x \) into \( y=-2x + 28 \)

Since both equations are solved for \( y \), we can set them equal to each other. So we substitute \( y \) in the first equation with \( 5x \) from the second equation. This gives us the equation \( 5x=-2x + 28 \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides of the equation \( 5x=-2x + 28 \) to get all the \( x \) terms on one side.
\( 5x+2x=-2x + 2x+ 28 \)
Simplifying both sides, we have \( 7x = 28 \).
Then divide both sides by 7: \( \frac{7x}{7}=\frac{28}{7} \), so \( x = 4 \).

Step3: Solve for \( y \)

Now that we know \( x = 4 \), we substitute \( x = 4 \) into the equation \( y = 5x \) (we could also use the other equation for \( y \)).
Substituting \( x = 4 \) into \( y = 5x \), we get \( y=5\times4 = 20 \).

Answer:

The solution to the system is \( x = 4 \) and \( y = 20 \), or as an ordered pair \( (4,20) \).