Solve the system by the substitution method. Be sure to check all proposed solutions. \[ \begin{array}{c} 4 x-y=4 \\ 9 x-2 y=10 \end{array} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \{\} . (Type an ordered pair.) B. There are infinitely many solutions. The solution set is $\{(x, y) \backslash\}$. (Type an equation.) C. There is no solution. The solution set is $\varnothing$

Step 1 ：First, we can express the first equation in terms of y: \(y = 4x - 4\).

Step 2 ：Then, we substitute \(y\) into the second equation: \(9x - 2(4x - 4) = 10\).

Step 3 ：Simplify the equation: \(9x - 8x + 8 = 10\), which simplifies to \(x + 8 = 10\).

Step 4 ：Solving for x, we get \(x = 10 - 8 = 2\).

Step 5 ：Substitute \(x = 2\) into the first equation to solve for y: \(y = 4*2 - 4 = 4\).

Step 6 ：Thus, the solution to the system of equations is \(\boxed{(2,4)}\).

Step 7 ：Check the solution by substituting \(x = 2\) and \(y = 4\) into both original equations to verify that both are true.