Solve for \( x \) and \( y \) \( 30 x-42 y=-6 \) \( 5 x-7 y=-1 \)

Solve the system of equations \( 30x-42y=-6;5x-7y=-1 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}30x-42y=-6\\5x-7y=-1\end{array}\right.\) - step1: Rearrange the terms: \(30x-42y=-6\) - step2: Move the expression to the right side: \(30x=-6+42y\) - step3: Divide both sides: \(\frac{30x}{30}=\frac{-6+42y}{30}\) - step4: Divide the numbers: \(x=\frac{-1+7y}{5}\) - step5: Calculate: \(\left(x,y\right) = \left(\frac{-1+7y}{5},y\right),y \in \mathbb{R}\) - step6: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations \(30x-42y=-6\) and \(5x-7y=-1\) has infinitely many solutions. This means that there are an infinite number of pairs of values for \(x\) and \(y\) that satisfy both equations simultaneously.