Systems of Two Linear Equations

Number sense systems are built to collapse in one step. Look first for a variable whose coefficients are equal and opposite — adding the equations eliminates it immediately.

For $ax + by = c$ and $dx - by = e$, adding gives $(a+d)x = c + e$, so $x = \frac{c+e}{a+d}$. Substitute back only if the question asks for the other variable.

If neither variable cancels directly, check whether one equation is a small multiple of the other before doing any real work.