Question

1. \\( 3y + 4x = 12 \\)\\( x = -y + 2 \\)

Explanation:

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

We know that \( x = -y + 2 \), so we replace \( x \) in the first equation with \( -y + 2 \).
The first equation is \( 3y + 4x = 12 \), substituting \( x \) gives:
\( 3y + 4(-y + 2) = 12 \)

Step2: Simplify the equation

First, distribute the 4 in \( 4(-y + 2) \):
\( 3y - 4y + 8 = 12 \)
Then, combine like terms \( 3y - 4y \):
\( -y + 8 = 12 \)

Step3: Solve for \( y \)

Subtract 8 from both sides of the equation:
\( -y = 12 - 8 \)
\( -y = 4 \)
Multiply both sides by -1 to solve for \( y \):
\( y = -4 \)

Step4: Solve for \( x \)

Now that we have \( y = -4 \), substitute \( y \) back into the equation \( x = -y + 2 \):
\( x = -(-4) + 2 \)
\( x = 4 + 2 \)
\( x = 6 \)

Answer:

The solution to the system of equations is \( x = 6 \) and \( y = -4 \), or the ordered pair \( (6, -4) \).