To determine if the point \((-4, 2)\) is a solution to the system of equations, we need to substitute \(x = -4\) and \(y = 2\) into both equations and check if both equations are satisfied.
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For the first equation: \[ y = \frac{1}{4}x + 1 \] Substituting \(x = -4\): \[ y = \frac{1}{4}(-4) + 1 = -1 + 1 = 0 \] But \(y\) should be \(2\), so this equation is not satisfied.
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For the second equation: \[ y = \frac{1}{2}x - 1 \] Substituting \(x = -4\): \[ y = \frac{1}{2}(-4) - 1 = -2 - 1 = -3 \] Again, this does not satisfy \(y = 2\).
Since \((-4, 2)\) does not satisfy either equation, the answer is no.