Rewrite into standard form: \( \begin{aligned} y-3 & =2(x+5) \\ y-3 & =2 x+10\end{aligned} \)

To rewrite the equations into standard form, we can follow these steps: Starting with the first equation: \[ y - 3 = 2(x + 5) \] Distributing the 2: \[ y - 3 = 2x + 10 \] Adding 3 to both sides gives: \[ y = 2x + 13 \] Rearranging into standard form (Ax + By = C): \[ -2x + y = 13 \quad \text{or equivalently} \quad 2x - y = -13 \] Now, for the second equation: \[ y - 3 = 2x + 10 \] Adding 3 to both sides gives: \[ y = 2x + 13 \] This is the same equation as before, which can also be written in standard form as: \[ 2x - y = -13 \] Finally, the standard form for both equations can be expressed collectively as: \[ 2x - y = -13 \]