1. **State the problem:** Solve the system of linear equations by substitution: $$4.51w = 13.14 - 2.33v$$ $$v = 7.23 - 1.63w$$ Find the value of $w$ rounded to 2 decimal places. 2. **Substitute $v$ from the second equation into the first:** $$4.51w = 13.14 - 2.33(7.23 - 1.63w)$$ 3. **Distribute $-2.33$:** $$4.51w = 13.14 - 2.33 \times 7.23 + 2.33 \times 1.63w$$ Calculate constants: $$2.33 \times 7.23 = 16.8459$$ $$2.33 \times 1.63 = 3.7979$$ So, $$4.51w = 13.14 - 16.8459 + 3.7979w$$ 4. **Simplify the right side:** $$4.51w = -3.7059 + 3.7979w$$ 5. **Bring terms with $w$ to one side:** $$4.51w - 3.7979w = -3.7059$$ $$0.7121w = -3.7059$$ 6. **Solve for $w$:** $$w = \frac{-3.7059}{0.7121} = -5.2049$$ 7. **Round to 2 decimal places:** $$w = -5.20$$