1. **State the problem:** We need to find the price of each regular pizza ($r$) and each deluxe pizza ($d$) given two orders. 2. **Set up the system of equations:** - Brendan's order: $10r + 2d = 120$ - Eliana's order: $7r + 2d = 96$ 3. **Use elimination to solve:** Subtract the second equation from the first to eliminate $d$: $$\cancel{10r} + 2d = 120$$ $$-\cancel{7r} - 2d = -96$$ ------------------- $$3r + 0 = 24$$ 4. **Solve for $r$:** $$3r = 24$$ $$r = \frac{24}{3} = 8$$ 5. **Substitute $r=8$ into one original equation to find $d$:** Using $7r + 2d = 96$: $$7(8) + 2d = 96$$ $$56 + 2d = 96$$ $$2d = 96 - 56 = 40$$ $$d = \frac{40}{2} = 20$$ 6. **Final answer:** Each regular pizza costs $8$, and each deluxe pizza costs $20$.