Solve using substitution \( \begin{array}{l}y=-2 x+2 \\ y=2 x+10\end{array} \)

To solve the system of equations using substitution, start with the first equation: \( y = -2x + 2 \). Now, substitute this expression for \( y \) into the second equation \( y = 2x + 10 \): \(-2x + 2 = 2x + 10\). Next, combine like terms: \(-2x - 2x = 10 - 2\), which simplifies to: \(-4x = 8\). Now, divide both sides by -4: \(x = -2\). Now that you have \( x \), substitute this value back into the first equation to find \( y \): \(y = -2(-2) + 2 = 4 + 2 = 6\). So, the solution to the system of equations is \( x = -2 \) and \( y = 6 \), or as an ordered pair, \((-2, 6)\). Now, if you want to verify, you can plug \( x = -2 \) back into the second equation to check if it gives the same \( y \): \(y = 2(-2) + 10 = -4 + 10 = 6\). Both equations agree with \( y = 6\), confirming our solution!