To evaluate the statements about the system of equations, let's first clarify the definitions:
- A consistent system has at least one solution (point of intersection).
- An inconsistent system has no solutions (the lines are parallel and never intersect).
- Lines that are parallel have the same slope and will never meet.
- Lines that are perpendicular intersect at a right angle and will have one solution.
Based on these definitions, we can analyze the provided statements.
Assuming the lines referred to in the system are:
- \( y = \frac{2}{3}x + 1 \) (Line A)
- \( y = -\frac{3}{2}x + 4 \) (Line B)
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The solution to the system is the point of intersection between lines \( e \) and \( f \). (Choosing lines A and B)
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The system is inconsistent because the lines are parallel. This would be incorrect for lines A and B since they are not parallel (they have different slopes).
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Since the lines are perpendicular, the system has a solution; consequently, they intersect at a point.
From this evaluation, the following statements can be regarded as true:
- The solution to the system is the point of intersection between lines (if referring to lines A and B).
- Since the lines are perpendicular, the system has a solution.
- It is impossible for y to equal both \( \frac{2}{3}x + 1 \) and \( -\frac{3}{2}x + 4 \) simultaneously; therefore the system has a solution. (This statement can be misunderstood depending on how it's phrased, but since the solution exists, we might clarify further).
So, the best three statements to choose, given the lines are perpendicular, would include those describing the solution through intersection and the nature of perpendicularity confirming that a solution exists. If you would specifically confirm the second and third statements, depending on the provided system details, that further validates the interaction of these equations.