To solve the system of linear equations:

1. $7x - 3y = 3$
2. $-21x + 9y = -5$

Step 1: Simplify the equations if possible

The second equation can be simplified by dividing through by $-3$:

$-21x + 9y = -5 \quad \rightarrow \quad 7x - 3y = \frac{5}{3}$

Now the system becomes:

1. $7x - 3y = 3$
2. $7x - 3y = \frac{5}{3}$

Step 2: Analyze the system

Since both equations have the same left-hand side but different right-hand sides ($3$ and $\frac{5}{3}$), the system is inconsistent. This means there are no solutions because the two equations represent parallel lines that never intersect.

Conclusion

The system of equations has no solution.

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Related Questions

1. What does it mean for a system of equations to be inconsistent?
2. How can you determine graphically that two lines are parallel?
3. What is the difference between dependent and inconsistent systems?
4. How would you solve these equations if they were consistent?
5. How can substitution or elimination methods reveal inconsistencies?

Tip: Always check if simplifying the equations reveals any contradictions or inconsistencies early on.