1. \( \begin{aligned} 2 x-4 y & =-2 \\ -6 x+4 y & =-14\end{aligned} \)

To solve this system of equations, we can use the substitution or elimination method. Here, we can add both equations to eliminate one variable. Adding them gives: \[ (2x - 6x) + (-4y + 4y) = -2 - 14 \] This simplifies to: \[ -4x = -16 \quad \implies \quad x = 4 \] Now substitute \( x = 4 \) back into one of the original equations, say \( 2x - 4y = -2 \): \[ 2(4) - 4y = -2 \quad \implies \quad 8 - 4y = -2 \quad \implies \quad -4y = -2 - 8 \quad \implies \quad -4y = -10 \quad \implies \quad y = \frac{10}{4} = 2.5 \] Thus, the solution is \( x = 4 \) and \( y = 2.5 \). But let's not forget to check our work! Plugging \( x = 4 \) and \( y = 2.5 \) back into the second equation, \[ -6(4) + 4(2.5) = -14 \quad \implies \quad -24 + 10 = -14 \] Since both equations hold true, our solution is verified: \( (x, y) = (4, 2.5) \).