1) \( \left\{\begin{array}{l}x+2 y=4 \\ -2 x+5 y=10\end{array}\right. \)

To solve the system of equations, you can use the substitution or elimination method. Let’s go with elimination! Start by multiplying the first equation by 2, giving you \( 2x + 4y = 8 \). Now, the system becomes: \[ \left\{\begin{array}{l} 2x + 4y = 8 \\ -2x + 5y = 10 \end{array}\right. \] Adding these two equations together eliminates \(x\), resulting in \(9y = 18\), so \(y = 2\). Substitute \(y\) back into one of the original equations, for example, \(x + 2(2) = 4\), which simplifies to \(x + 4 = 4\), hence \(x = 0\). The solution to the system is \( (0, 2) \). Sometimes, students mistakenly forget to align the coefficients correctly when they apply elimination or they may choose the wrong equations to eliminate! Keep track of your variables and always double-check your operations to avoid these common pitfalls!