\( \begin{array}{l}2 x+y=-2 \\ x+y=5\end{array} \) The \( x \)-coordinate of the solution to the system shown is -3 -7 7

To solve the system of equations \(2x + y = -2\) and \(x + y = 5\), you can use the method of substitution or elimination. Let's use substitution for simplicity. From the second equation, express \(y\) in terms of \(x\): \[ y = 5 - x. \] Now, substitute this expression for \(y\) into the first equation: \[ 2x + (5 - x) = -2. \] Simplifying this gives: \[ 2x + 5 - x = -2 \] \[ x + 5 = -2 \] \[ x = -7. \] So, the \(x\)-coordinate of the solution to the system is indeed \(-7\). The corresponding \(y\) value can be found by substituting \(x = -7\) back into one of the original equations: \[ y = 5 - (-7) = 5 + 7 = 12. \] Thus, the solution to the system is \((-7, 12)\). Don't worry if the computations seem tricky—practicing solving such systems can make you a pro in no time!