To solve the system of equations:
- \(-x + 6y = 13\) (Equation 1)
- \(4x - 10y = -10\) (Equation 2)
We can use the substitution or elimination method. Here, we'll use the substitution method.
First, we can solve Equation 1 for \(x\):
\[ -x + 6y = 13 \implies -x = 13 - 6y \implies x = 6y - 13 \]
Now, we can substitute this expression for \(x\) into Equation 2:
\[ 4(6y - 13) - 10y = -10 \]
Expanding the left side:
\[ 24y - 52 - 10y = -10 \]
Combining like terms:
\[ 14y - 52 = -10 \]
Adding 52 to both sides:
\[ 14y = 42 \]
Dividing both sides by 14:
\[ y = 3 \]
Now, substitute \(y = 3\) back into the expression we found for \(x\):
\[ x = 6(3) - 13 = 18 - 13 = 5 \]
So, we have:
\[ x = 5, , y = 3 \]
The solution to the system of equations is:
\[ (x, y) = (5, 3) \]
Thus, the final answer is:
\[ (5, 3) \]