To determine if the points (0, 2) and (0, -4) are solutions to the system of linear equations \(y = 2x + 2\) and \(y = 2x - 4\), we can substitute the \(x\) values of the points into both equations and see if we get the corresponding \(y\) values.
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For the point (0, 2):
- Substitute \(x = 0\) into the first equation: \[ y = 2(0) + 2 = 2 \] This matches the \(y\) value of the point (0, 2).
- Substitute \(x = 0\) into the second equation: \[ y = 2(0) - 4 = -4 \] This does not match the \(y\) value of the point (0, 2).
Thus, (0, 2) is a solution to the first equation but not to the second.
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For the point (0, -4):
- Substitute \(x = 0\) into the first equation: \[ y = 2(0) + 2 = 2 \] This does not match the \(y\) value of the point (0, -4).
- Substitute \(x = 0\) into the second equation: \[ y = 2(0) - 4 = -4 \] This matches the \(y\) value of the point (0, -4).
Thus, (0, -4) is a solution to the second equation but not to the first.
Given this analysis:
- The point (0, 2) is a solution to \(y = 2x + 2\), but not to \(y = 2x - 4\).
- The point (0, -4) is a solution to \(y = 2x - 4\), but not to \(y = 2x + 2\).
Final Answer: Neither of these points are solutions to the system of equations.