Given the line \( -52 x+(-8) y=-596 \) and when \( y=-2 \), find the value of \( x \). Please round your final answer to two decimal places.

To find the value of \( x \) when \( y = -2 \), we start by substituting \( y \) into the equation: \[ -52 x + (-8)(-2) = -596 \] Calculating \( (-8)(-2) \) gives us \( 16 \). Now we have: \[ -52 x + 16 = -596 \] Next, we isolate the term with \( x \): \[ -52 x = -596 - 16 \] Calculating the right side: \[ -596 - 16 = -612 \] Now we have: \[ -52 x = -612 \] Dividing both sides by \( -52 \): \[ x = \frac{-612}{-52} = \frac{612}{52} \] Now, simplifying \( \frac{612}{52} \): \[ \frac{612 \div 4}{52 \div 4} = \frac{153}{13} \approx 11.76923076923077 \] Rounding to two decimal places, we get: \[ x \approx 11.77 \] So, the value of \( x \) when \( y = -2 \) is **11.77**.