1. **State the problem:** We are given two equations: $$y = \frac{27}{2} = -3x$$ and $$27 = 9y - 2x$$ We need to analyze and solve these equations. 2. **Clarify the first equation:** The first equation seems to have an equality chain: $$y = \frac{27}{2} = -3x$$. This means: $$y = \frac{27}{2}$$ and $$\frac{27}{2} = -3x$$ 3. **Solve for $x$ from the first equation:** From $$\frac{27}{2} = -3x$$, we isolate $x$: $$x = -\frac{27}{2 \times 3} = -\frac{27}{6} = -\frac{9}{2}$$ 4. **Substitute $y$ and $x$ into the second equation:** The second equation is: $$27 = 9y - 2x$$ Substitute $y = \frac{27}{2}$ and $x = -\frac{9}{2}$: $$27 = 9 \times \frac{27}{2} - 2 \times \left(-\frac{9}{2}\right)$$ 5. **Simplify the right side:** $$9 \times \frac{27}{2} = \frac{243}{2}$$ $$-2 \times \left(-\frac{9}{2}\right) = 9$$ So, $$27 = \frac{243}{2} + 9$$ 6. **Convert to common denominator and sum:** $$9 = \frac{18}{2}$$ So, $$\frac{243}{2} + \frac{18}{2} = \frac{261}{2}$$ 7. **Check equality:** Left side is 27, right side is $$\frac{261}{2} = 130.5$$ Since $$27 \neq 130.5$$, the two equations are inconsistent with the given values. **Final conclusion:** The given system has no solution because substituting $y = \frac{27}{2}$ and $x = -\frac{9}{2}$ into the second equation does not satisfy it. **Summary:** - From the first equation, $y = \frac{27}{2}$ and $x = -\frac{9}{2}$. - Substituting into the second equation yields a contradiction. Hence, the system is inconsistent.