Solve the system of equations. $-10 x+3 y=5 ; x=y-4$

Step 1 ：The system of equations is given as $-10 x+3 y=5$ and $x=y-4$. The goal is to find the values of x and y that satisfy both equations simultaneously.

Step 2 ：Since the second equation is already solved for x, we can use the substitution method. This involves substitifying the expression for one variable from one equation into the other equation.

Step 3 ：Substitute $x = y - 4$ from the second equation into the first equation. This will give us an equation in terms of y only, which we can then solve for y.

Step 4 ：The substituted equation is $40 - 7y = 5$. Solving this equation gives the solution for y as $y = 5$.

Step 5 ：Once we have the value of y, we can substitute it back into the second equation to find the value of x. Substituting $y = 5$ into the equation $x = y - 4$ gives the solution for x as $x = 1$.

Step 6 ：\(\boxed{x = 1, y = 5}\) is the solution to the system of equations.