Question

solve the system by substitution.

y = -2x + 30
y = 4x

Explanation:

Step1: Substitute \( y = 4x \) into \( y=-2x + 30 \)

Since both equations are solved for \( y \), we can substitute the expression for \( y \) from the second equation into the first. So we get \( 4x=-2x + 30 \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides of the equation \( 4x=-2x + 30 \) to get \( 4x + 2x=-2x+2x + 30 \), which simplifies to \( 6x = 30 \). Then divide both sides by 6: \( x=\frac{30}{6}=5 \).

Step3: Substitute \( x = 5 \) into \( y = 4x \)

Now that we have \( x = 5 \), we substitute it into the equation \( y = 4x \). So \( y=4\times5 = 20 \).

Answer:

The solution to the system is \( x = 5 \) and \( y = 20 \), or as an ordered pair \( (5,20) \).