Subjects algebra

Linear Equations Cf6508

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Linear Equations Cf6508


1. **State the problem:** Solve the system of linear equations: $$2x + y = 17$$ $$-18x + 9y = ?$$ Since the second equation is incomplete, we will focus on the first equation and analyze the relationship between the two. 2. **Rewrite the first equation:** $$y = 17 - 2x$$ 3. **Check if the second equation is a multiple of the first:** Multiply the first equation by $-9$: $$-9(2x + y) = -9(17)$$ $$-18x - 9y = -153$$ 4. **Compare with the second equation:** The second equation is $-18x + 9y = ?$ but from the multiplication, we get $-18x - 9y = -153$. 5. **Conclusion:** The second equation as given is inconsistent with the first equation multiplied by $-9$ because of the sign difference in $y$ term. If the second equation were $-18x - 9y = -153$, it would be dependent on the first. Since the second equation is incomplete, we cannot solve the system fully. **Final answer:** The system cannot be solved without the complete second equation.