Solve the following system of equations. Express your answer as an ordered pair in the format \( (a, b) \), with no spaces between the numbers or symbols. \( \begin{array}{l}2 x+7 y=-7 \\ -4 x-3 y=-19\end{array} \)

To solve the system of equations, we can use the method of substitution or elimination. Let's use elimination. Given the equations: 1. \(2x + 7y = -7\) (Equation 1) 2. \(-4x - 3y = -19\) (Equation 2) First, we'll multiply Equation 1 by 2 to make the coefficients of \(x\) in both equations opposites: \(2(2x + 7y) = 2(-7)\) This gives us: \(4x + 14y = -14\) (Equation 3) Now we have: 1. \(4x + 14y = -14\) (Equation 3) 2. \(-4x - 3y = -19\) (Equation 2) Next, we add Equations 3 and 2: \((4x + 14y) + (-4x - 3y) = -14 - 19\) This simplifies to: \(11y = -33\) Now, divide both sides by 11: \(y = -3\) Now that we have \(y\), we can substitute it back into Equation 1 to find \(x\): \(2x + 7(-3) = -7\) This simplifies to: \(2x - 21 = -7\) Adding 21 to both sides gives us: \(2x = 14\) Now, divide by 2: \(x = 7\) Thus, the solution to the system of equations is: \((7,-3)\)