What is the resulting equation when the expression for \( y \) in the second equation is substituted into the first equation? \[ \begin{array}{l} 3 x+y=1 \\ y=6-4 x \end{array} \] \( -x+6=1 \) \( 7 x+6=1 \) \( x+6=1 \)

When you substitute the expression for \( y \), which is \( 6 - 4x \), into the first equation \( 3x + y = 1 \), you get: \[ 3x + (6 - 4x) = 1. \] Simplifying this leads to \( 3x + 6 - 4x = 1 \), which simplifies to \( -x + 6 = 1 \). So, you're left with a straightforward linear equation! To isolate \( x \), you can rearrange the equation. Subtracting 6 from both sides gives: \[ -x = 1 - 6, \] which simplifies to \( -x = -5 \), leading to \( x = 5 \). Now, isn't that a neat twist? You had a system of equations, and with a little substitution, you discovered the solution!