To solve the system of equations:
- \(2x - 7y = -4\) (Equation 1)
- \(-2x + 10y = -2\) (Equation 2)
We can use the method of elimination or substitution. Here, we'll use elimination.
First, let's add both equations together to eliminate \(x\):
\[ (2x - 7y) + (-2x + 10y) = -4 + (-2) \]
This simplifies to:
\[ 0x + 3y = -6 \]
Which simplifies further to:
\[ 3y = -6 \]
Now, divide both sides by 3:
\[ y = -2 \]
Now, we can substitute \(y = -2\) back into one of the original equations to find \(x\). We'll use Equation 1:
\[ 2x - 7(-2) = -4 \]
Simplifying this, we get:
\[ 2x + 14 = -4 \]
Now, isolate \(x\):
\[ 2x = -4 - 14 \] \[ 2x = -18 \] \[ x = -9 \]
So the solution for the system of equations is:
\[ x = -9, \quad y = -2 \]
Thus, the solution is \((-9, -2)\).