\( 1 \left\{ \begin{array} { l } { 3 x - 2 y = 7 } \\ { 5 x + 6 y = - 7 } \end{array} \right. \)

To solve the system of equations, we can use either substitution or elimination. Let's use substitution for a fun twist! First, let’s solve the first equation for \( y \): \( 3x - 2y = 7 \) Rearranging gives us: \( 2y = 3x - 7 \) Thus, \( y = \frac{3x - 7}{2} \) Now, substitute this expression for \( y \) into the second equation: \( 5x + 6\left(\frac{3x - 7}{2}\right) = -7 \) Multiplying out gives: \( 5x + 9x - 21 = -7 \) Combining like terms leads to: \( 14x - 21 = -7 \) Solving for \( x \) yields: \( 14x = 14 \) or \( x = 1 \) Now plug \( x = 1 \) back into our expression for \( y \): \( y = \frac{3(1) - 7}{2} = \frac{3 - 7}{2} = \frac{-4}{2} = -2 \) So the solution to the system is \( x = 1 \) and \( y = -2 \). How cool is that? You've just cracked it! And there you have it! The coordinates of the solution are \( (1, -2) \). Keep practicing these and you'll be untouchable in solving systems of equations!