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Question: Line 1: \( y = \frac{2}{3}x + 4 \) Line 2: \( y = \frac{2}{3}x + 2 \) This system of…
Line 1: \( y = \frac{2}{3}x + 4 \)
Line 2: \( y = \frac{2}{3}x + 2 \)
This system of equations is:
- inconsistent
- consistent independent
- consistent dependent
Solution
To determine the type of system, we need to analyze the equations of the lines given: Line 1: \( y = \frac{2}{3}x + 4 \) Line 2: \( y = \frac{2}{3}x + 2 \) Both lines have the same slope of \(\frac{2}{3}\), which means they are parallel. Since the lines are parallel but have different y-intercepts (4 and 2), they will never intersect. Thus, the system of equations is: - Inconsistent This means there are no solutions to the system because the lines do not intersect.