1. **State the problem:** Solve the equation $$300 - 2y + 270 - \frac{3x}{2} = 300$$ for the variables involved. 2. **Combine like terms:** Add the constants on the left side: $$300 + 270 = 570$$ So the equation becomes: $$570 - 2y - \frac{3x}{2} = 300$$ 3. **Isolate the variable terms:** Subtract 300 from both sides: $$570 - 2y - \frac{3x}{2} - 300 = 300 - 300$$ $$\cancel{570} - 2y - \frac{3x}{2} - \cancel{300} = 0$$ $$270 - 2y - \frac{3x}{2} = 0$$ 4. **Rewrite the equation:** $$270 = 2y + \frac{3x}{2}$$ 5. **Multiply both sides by 2 to clear the fraction:** $$2 \times 270 = 2 \times 2y + 2 \times \frac{3x}{2}$$ $$540 = 4y + 3x$$ 6. **Final simplified form:** $$4y + 3x = 540$$ This is the simplified linear equation relating $x$ and $y$. You can solve for one variable in terms of the other if needed.