1. **State the problem:** Solve the system of equations by substitution: $$4.51w = 13.14 - 2.33v$$ $$v = 7.23 - 1.63w$$ Find the value of $v$ rounded to 2 decimal places. 2. **Use substitution:** From the second equation, we have $v$ in terms of $w$: $$v = 7.23 - 1.63w$$ 3. **Substitute $v$ into the first equation:** $$4.51w = 13.14 - 2.33(7.23 - 1.63w)$$ 4. **Expand and simplify:** $$4.51w = 13.14 - 2.33 \times 7.23 + 2.33 \times 1.63w$$ $$4.51w = 13.14 - 16.8459 + 3.7979w$$ 5. **Combine like terms:** $$4.51w - 3.7979w = 13.14 - 16.8459$$ $$0.7121w = -3.7059$$ 6. **Solve for $w$:** $$w = \frac{-3.7059}{0.7121} = -5.2047$$ 7. **Substitute $w$ back to find $v$:** $$v = 7.23 - 1.63 \times (-5.2047) = 7.23 + 8.4797 = 15.7097$$ 8. **Round $v$ to 2 decimal places:** $$v = 15.71$$