1. **State the problem:** Solve the system of equations by elimination: $$21x + 15y = 3$$ $$7x + 5y = 1$$ 2. **Explain the elimination method:** We want to eliminate one variable by making the coefficients of that variable the same (or opposites) in both equations, then subtract or add the equations. 3. **Make coefficients of $y$ the same:** Multiply the second equation by 3 to match the coefficient of $y$ in the first equation: $$3 \times (7x + 5y) = 3 \times 1$$ $$21x + 15y = 3$$ 4. **Write the new system:** $$21x + 15y = 3$$ $$21x + 15y = 3$$ 5. **Subtract the second equation from the first:** $$ (21x + 15y) - (21x + 15y) = 3 - 3 $$ $$ 0 = 0 $$ 6. **Interpretation:** The subtraction results in a true statement $0=0$, which means the two equations are dependent and represent the same line. 7. **Conclusion:** There are infinitely many solutions along the line defined by either equation. The system is dependent. 8. **Express the solution:** Solve one equation for $y$ in terms of $x$: From the second equation: $$7x + 5y = 1$$ $$5y = 1 - 7x$$ $$y = \frac{1 - 7x}{5}$$ **Final answer:** $$y = \frac{1 - 7x}{5}$$ This represents infinitely many solutions along this line.