## Problem Solve the system: $2x+3y=7$ $x-y=1$ Find $x+y$. ## Method (substitution) 1. Start with the second equation: $x-y=1$ 2. Solve for $x$ in terms of $y$: $x-y+ y=1+ y$ $x=1+y$ 3. Substitute $x=1+y$ into the first equation $2x+3y=7$: $2(1+y)+3y=7$ 4. Distribute and combine like terms: $2+2y+3y=7$ $2+5y=7$ 5. Subtract $2$ from both sides (show cancel line): $\;\;\cancel{2}+5y=\;\;\cancel{2}+7$ $5y=5$ 6. Divide both sides by $5$ (show cancel line): $\;\;\cancel{5}y=\;\;\cancel{5}$ $y=1$ 7. Plug $y=1$ back into $x=1+y$: $x=1+1$ $x=2$ 8. Compute $x+y$: $x+y=2+1$ $x+y=3$