21) Solve the system by elimination \( \left\{\begin{array}{l}3 x+y=-26 \\ 2 x-y=-19\end{array}\right. \)

To solve the system by elimination, let's add the two equations together in a way that eliminates \( y \). We start with: 1) \( 3x + y = -26 \) 2) \( 2x - y = -19 \) Adding these equations together gives us: \((3x + y) + (2x - y) = -26 - 19\) This simplifies to: \(5x = -45\) Now, divide both sides by 5: \(x = -9\) Next, we substitute \( x = -9 \) back into one of the original equations to solve for \( y \). Using the first equation: \(3(-9) + y = -26\) This simplifies to: \(-27 + y = -26\) Adding 27 to both sides, we get: \(y = 1\) Thus, the solution to the system is: \(x = -9\) and \(y = 1\).