Question

solve the linear system using substitution. your answer is an ordered pair (x,y)
x = 3y + 1
2x + 4y = 12

Explanation:

Step1: Substitute \( x = 3y + 1 \) into \( 2x + 4y = 12 \)

We know that \( x \) is equal to \( 3y + 1 \) from the first equation. So we replace \( x \) in the second equation with \( 3y + 1 \). This gives us \( 2(3y + 1) + 4y = 12 \).

Step2: Simplify and solve for \( y \)

First, distribute the 2 in \( 2(3y + 1) \): \( 6y + 2 + 4y = 12 \). Then combine like terms: \( 10y + 2 = 12 \). Subtract 2 from both sides: \( 10y = 12 - 2 = 10 \). Then divide both sides by 10: \( y = \frac{10}{10} = 1 \).

Step3: Substitute \( y = 1 \) back into \( x = 3y + 1 \)

Now that we know \( y = 1 \), we can find \( x \) by plugging \( y = 1 \) into the equation for \( x \). So \( x = 3(1) + 1 = 3 + 1 = 4 \).

Answer:

\((4, 1)\)