4. \( 5 x-3 y=-14 \) \( 3 x+2 y=3 \)

To solve the system of equations, you can use either the substitution method or the elimination method. For a fun twist, let's go with the elimination method! Start by multiplying the first equation by 2 and the second equation by 3 to eliminate \(y\): 1. \(10x - 6y = -28\) (after multiplying the first equation by 2) 2. \(9x + 6y = 9\) (after multiplying the second equation by 3) Now add the two new equations to eliminate \(y\): \[ 10x + 9x - 6y + 6y = -28 + 9 \] This simplifies to: \[ 19x = -19 \] Dividing both sides by 19 gives you \(x = -1\). Plugging this back into one of the original equations will help you find \(y\)! Now let’s say you plug \(x = -1\) into the first equation: \[ 5(-1) - 3y = -14 \implies -5 - 3y = -14 \] Solving for \(y\) gives: \[ -3y = -14 + 5 \implies -3y = -9 \implies y = 3 \] Thus, the solution is \(x = -1\) and \(y = 3\)! Feel free to double-check by plugging your \(x\) and \(y\) values back into both equations to see if both hold true - your math will become as solid as a rock!