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Which describes the system of equations below?\newliney=52x+95y = \frac{5}{2}x + \frac{9}{5}\newliney=52x+54y = \frac{5}{2}x + \frac{5}{4}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent

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Full solution

Q. Which describes the system of equations below?\newliney=52x+95y = \frac{5}{2}x + \frac{9}{5}\newliney=52x+54y = \frac{5}{2}x + \frac{5}{4}\newlineChoices:\newline(A)consistent and dependent\newline(B)inconsistent\newline(C)consistent and independent
  1. Determine System Type: To determine the type of system, we need to compare the slopes and yy-intercepts of the two equations.
  2. Slope-Intercept Form: The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  3. First Equation Analysis: For the first equation y=52x+95y = \frac{5}{2}x + \frac{9}{5}, the slope (mm) is 52\frac{5}{2} and the y-intercept (bb) is 95\frac{9}{5}.
  4. Second Equation Analysis: For the second equation y=52x+54y = \frac{5}{2}x + \frac{5}{4}, the slope (mm) is also 52\frac{5}{2} and the y-intercept (bb) is 54\frac{5}{4}.
  5. Parallel Lines Conclusion: Since both equations have the same slope but different yy-intercepts, the lines are parallel and will never intersect.
  6. Inconsistent System: Parallel lines that never intersect mean that there is no solution to the system of equations, making it inconsistent.

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