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 $\varnothing$

Answer

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Answer

Check the solution by substituting $x = 2$ and $y = 4$ into both original equations to verify that both are true.

Steps

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.