\( \left. \begin{array} { l } { 2 x + 4 y = 20 \ldots \ldots . . . } \\ { 7 x - 3 y = 19 \ldots \ldots . . } \end{array} \right. \)

Let's solve the system of equations step by step! First, we take the equation \(2x + 4y = 20\) and simplify it by dividing everything by 2, yielding \(x + 2y = 10\). Now, we can express \(x\) in terms of \(y\): \(x = 10 - 2y\). Now we substitute \(x\) into the second equation \(7x - 3y = 19\): \[ 7(10 - 2y) - 3y = 19 \] This simplifies to: \[ 70 - 14y - 3y = 19 \] Combining like terms gives: \[ 70 - 17y = 19 \] Subtracting 70 from both sides results in: \[ -17y = 19 - 70 \rightarrow -17y = -51 \] Now, divide by -17: \[ y = 3 \] With \(y\) found, substitute back to find \(x\): \[ x = 10 - 2(3) = 10 - 6 = 4 \] Thus, the solution to the system of equations is \(x = 4\) and \(y = 3\). Final solution: \[ (x, y) = (4, 3) \]