To solve the system of equations:
- \(3x - 2y = -14\) (Equation 1)
- \(3x - 8y = -2\) (Equation 2)
We can use the elimination method. First, let's subtract Equation 1 from Equation 2 to eliminate \(3x\).
\[ (3x - 8y) - (3x - 2y) = -2 - (-14) \]
This simplifies to:
\[ -8y + 2y = -2 + 14 \]
\[ -6y = 12 \]
Now, divide both sides by -6:
\[ y = -2 \]
Now that we have the value of \(y\), we can substitute it back into Equation 1 to solve for \(x\):
\[ 3x - 2(-2) = -14 \]
This simplifies to:
\[ 3x + 4 = -14 \]
Now, subtract 4 from both sides:
\[ 3x = -14 - 4 \]
\[ 3x = -18 \]
Now, divide both sides by 3:
\[ x = -6 \]
Thus, the solution to the system of equations is:
\[ x = -6, \quad y = -2. \]
So, the ordered pair \((-6, -2)\) is the solution.
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