Question

solve the system by substitution.

$y = 4x + 6$
$y = 7x$

Explanation:

Step1: Substitute \( y = 7x \) into \( y = 4x + 6 \)

Since both equations equal \( y \), we can set them equal to each other. So we substitute \( y \) in the first equation with \( 7x \) from the second equation. This gives us \( 7x = 4x + 6 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides of the equation \( 7x = 4x + 6 \).
\( 7x - 4x = 4x + 6 - 4x \)
Simplifying both sides, we get \( 3x = 6 \). Then divide both sides by 3: \( \frac{3x}{3}=\frac{6}{3} \), so \( x = 2 \).

Step3: Solve for \( y \)

Now that we know \( x = 2 \), we substitute \( x = 2 \) into the equation \( y = 7x \). So \( y = 7\times2 = 14 \).

Answer:

The solution to the system is \( x = 2 \) and \( y = 14 \), or as an ordered pair \( (2, 14) \).