3. Is $(3,-5)$ the solution for the following linear system? Explain how you can tell.
\[
\begin{array}{l}
2 x+5 y=-19 \\
6 y-8 x=54
\end{array}
\]
Answer
\(\boxed{\text{No, (3,-5) is not a solution to the system of equations.}}\)
Step 1 ：Given the point (3,-5), we substitute these values into the system of equations.
Step 2 ：For the first equation, \(2x + 5y = -19\), substituting x = 3 and y = -5, we get \(2*3 + 5*(-5) = -19\), which is true.
Step 3 ：For the second equation, \(6y - 8x = 54\), substituting x = 3 and y = -5, we get \(6*(-5) - 8*3 = -54\), which is not equal to 54.
Step 4 ：Since the point (3,-5) does not satisfy both equations, it is not a solution to the system of equations.
Step 5 ：\(\boxed{\text{No, (3,-5) is not a solution to the system of equations.}}\)
