To add the equations \(3x - y = -1\) and \(-3x + 3y = 27\), we can follow these steps:
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Write the equations: \[ 3x - y = -1 \quad \text{(Equation 1)} \] \[ -3x + 3y = 27 \quad \text{(Equation 2)} \]
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Add the left-hand sides and the right-hand sides: \[ (3x - y) + (-3x + 3y) = -1 + 27 \]
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Simplify the left-hand side: \[ 3x - 3x - y + 3y = 0 + 2y = 2y \]
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Simplify the right-hand side: \[ -1 + 27 = 26 \]
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The combined equation is: \[ 2y = 26 \]
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Now, we can solve for \(y\): \[ y = \frac{26}{2} = 13 \]
Thus, adding the two equations results in the equation \(2y = 26\) and leads to \(y = 13\).