Solve the following system of equations by the elimination method. Check your solution.
\[
\left\{\begin{array}{l}
x+5 y=-15 \\
5 x+3 y=13
\end{array}\right.
\]
Select the correct choice below and fill in any answer boxes present in your choice.
A. There is one solution. The solution set is (Simplify your answer. Type an ordered pair.)
B. There are infinitely many solutions. The solution set is the set of all ordered pairs $\left\{\left(x_{1}\right)\right\}$, where $x$ is any real number.
(Type an expression using $x$ as the variable.)
c. The solution set is the empty set.
Answer
The solution to the system of equations is \(\boxed{(5, -4)}\).
Step 1 ：Multiply the first equation by 5 and the second equation by 1 to get two new equations: 5x + 25y = -75 and 5x + 3y = 13.
Step 2 ：Subtract the second equation from the first to eliminate y: 22y = -88.
Step 3 ：Divide both sides of the equation by 22 to solve for y: y = -4.
Step 4 ：Substitute y = -4 into the first original equation to solve for x: x + 5*(-4) = -15, which simplifies to x = 5.
Step 5 ：The solution to the system of equations is \(\boxed{(5, -4)}\).
