Step 1 :The given system of equations is: \[\begin{aligned} 4 x-3 y & =-5 \\ -8 x+6 y & =10 \end{aligned}\]
Step 2 :We can see that the second equation is just the first equation multiplied by -2. This means that the two equations are dependent and represent the same line.
Step 3 :Therefore, there are infinitely many solutions to this system of equations. However, we can still find the general form of the solutions.
Step 4 :The solution to the system of equations is given by the expression \(x = \frac{3y}{4} - \frac{5}{4}\). This means that for any real number \(y\), we can find a corresponding \(x\) that satisfies both equations.
Step 5 :\(\boxed{\text{Final Answer: There are infinitely many solutions. The solution is }\left(\frac{3y}{4} - \frac{5}{4}, y\right)\text{, where } y \text{ is any real number.}}\)