1. The problem: You asked if, after finding values for $x$ and $y$ in a linear system, you need to plug them back into the equations. 2. Explanation: In solving linear systems, once you find values for $x$ and $y$, it is important to verify your solution by substituting these values back into the original equations. 3. Why verify? This step ensures that the values satisfy both equations, confirming your solution is correct. 4. How to verify: Take your found values $x = a$ and $y = b$, and substitute into each equation. 5. Example: If the system is $$\begin{cases} 2x + 3y = 7 \\ x - y = 1 \end{cases}$$ and you find $x=2$, $y=1$, substitute: $$2(2) + 3(1) = 4 + 3 = 7$$ $$2 - 1 = 1$$ Both true, so solution is correct. 6. Summary: Always plug your solution back into the original equations to confirm correctness.