Step 1 :Given the system of equations: \[\begin{array}{c} 3 x-3 y=10 \\ -2 x+y=-4 \end{array}\]
Step 2 :Express one variable in terms of the other from one equation. From the first equation, we can express y in terms of x: \[y = x - \frac{10}{3}\]
Step 3 :Substitute this expression into the second equation: \[-2x + (x - \frac{10}{3}) = -4\]
Step 4 :Solve this equation for x to get: \[x = \frac{2}{3}\]
Step 5 :Substitute x = \frac{2}{3} back into the first equation to solve for y: \[y = -\frac{8}{3}\]
Step 6 :Final Answer: The solution is \(\boxed{(\frac{2}{3}, -\frac{8}{3})}\)