To solve the system of equations:
- \(-x + 6y = 13\) (Equation 1)
- \(4x - 10y = -10\) (Equation 2)
We can use either substitution or elimination. Here, I'll use the substitution method.
First, let's solve Equation 1 for \(x\):
\[ -x + 6y = 13 \]
Add \(x\) to both sides:
\[ 6y = x + 13 \]
Now, let's isolate \(x\):
\[ x = 6y - 13 \]
Now, we can substitute \(x\) in Equation 2:
\[ 4(6y - 13) - 10y = -10 \]
Distribute \(4\):
\[ 24y - 52 - 10y = -10 \]
Combine like terms:
\[ (24y - 10y) - 52 = -10 \] \[ 14y - 52 = -10 \]
Now, add \(52\) to both sides:
\[ 14y = 42 \]
Now, divide by \(14\):
\[ y = 3 \]
Now that we have \(y\), substitute it back into the equation for \(x\):
\[ x = 6(3) - 13 \] \[ x = 18 - 13 \] \[ x = 5 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (5, 3) \]
So the answer is \((5, 3)\).
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