Use the substitution method to solve the system
\[
\left\{\begin{array}{l}
-x+y=-6 \\
4 x-3 y=21
\end{array}\right.
\]

Answer

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Answer

Final Answer: The solution to the system of equations is \(\boxed{x = 3, y = -3}\)

Steps

Step 1 ：Solve the first equation for y in terms of x: \(y = x + 6\)

Step 2 ：Substitute \(y = x + 6\) into the second equation: \(4x - 3(x + 6) = 21\)

Step 3 ：Solve for x: \(x = 3\)

Step 4 ：Substitute \(x = 3\) back into the first equation to find y: \(-3 + y = -6\)

Step 5 ：Solve for y: \(y = -3\)

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{x = 3, y = -3}\)