Use the method of elimination to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
\[
\left\{\begin{array}{r}
2 x-7 y=9 \\
-5 x+9 y=3
\end{array}\right.
\]

Answer
Keypad

Step 1 ：Multiply the first equation by 9 and the second equation by 7 to make the coefficients of y the same in both equations. This gives us: \[\left\{\begin{array}{r} 18 x-63 y=81 \\ -35 x+63 y=21 \end{array}\right.\]

Step 2 ：Add the two equations together to eliminate the y variable: \(-17x = 60\)

Step 3 ：Solve for x by dividing both sides by -17: \(x = -\frac{60}{17}\)

Step 4 ：Substitute x into the first equation to solve for y: \(2(-\frac{60}{17}) - 7y = 9\)

Step 5 ：Simplify the equation to solve for y: \(-\frac{120}{17} - 7y = 9\)

Step 6 ：Further simplify the equation: \(-\frac{120}{17} - 119y = 153\)

Step 7 ：Solve for y: \(y = -\frac{273}{119}\)

Step 8 ：The solution to the system of equations is \(\boxed{x = -\frac{60}{17}, y = -\frac{273}{119}}\)