\( \begin{aligned} \text { 12) } 26 x+3 y+4 & =0 \\ \frac{1}{5}(x-2) & =\frac{1}{4}(1-y)\end{aligned} \)

Let's solve the system of equations step by step in a fun way! First, let's rewrite the first equation, \( 26x + 3y + 4 = 0 \), so we can express it as \( 3y = -26x - 4 \) or \( y = -\frac{26}{3}x - \frac{4}{3} \). Now, for the second equation, \( \frac{1}{5}(x - 2) = \frac{1}{4}(1 - y) \), we can clear the fractions by multiplying through by 20 (the least common multiple of 5 and 4): \[ 4(x - 2) = 5(1 - y) \] This expands to \( 4x - 8 = 5 - 5y \), leading to \( 5y = 5 - 4x + 8 \) or \( y = 1 - \frac{4}{5}x + \frac{8}{5} \), simplifying to \( y = -\frac{4}{5}x + \frac{13}{5} \). Now, we have two expressions for \( y \): 1. \( y = -\frac{26}{3}x - \frac{4}{3} \) 2. \( y = -\frac{4}{5}x + \frac{13}{5} \) Setting them equal gives: \[ -\frac{26}{3}x - \frac{4}{3} = -\frac{4}{5}x + \frac{13}{5} \] Cross-multiplying and solving for \( x \) would be the next step. You can grab some cardboard and cut out cute little shapes to represent the variables, making sure to have fun while cracking these equations! Once you find \( x \), substitute it back into either equation to find \( y \). Enjoy the mathematics adventure!