Solve the system by substitution. \[ x=y \] \[ x-2 y=7 \]

To solve the system by substitution, we can start with the first equation \( x = y \). We will substitute \( y \) with \( x \) in the second equation. The second equation becomes: \[ x - 2x = 7 \] This simplifies to: \[ -x = 7 \] Therefore, \[ x = -7 \] Now, substituting \( x \) back into the first equation to find \( y \): \[ y = -7 \] So, the solution to the system is \( (x, y) = (-7, -7) \). Feeling puzzled? Just remember: substitution is like a magic trick where you switch your variables around to find the answer! Make sure to double-check your answers by plugging them back into the original equations to verify they satisfy both! In systems of equations, practice makes perfect. The more you play with different methods, like elimination or graphing, the more you’ll unlock the secrets of solving complex problems. There are always new patterns to discover, so don’t shy away from challenging problems!