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Which describes the system of equations below?\newliney=−75x+710y = -\frac{7}{5}x + \frac{7}{10}\newliney=43x−95y = \frac{4}{3}x - \frac{9}{5}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent

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Q. Which describes the system of equations below?\newliney=−75x+710y = -\frac{7}{5}x + \frac{7}{10}\newliney=43x−95y = \frac{4}{3}x - \frac{9}{5}\newlineChoices:\newline(A)inconsistent\newline(B)consistent and independent\newline(C)consistent and dependent
  1. Compare Slopes and Intercepts: To determine the type of system represented by the two equations, we need to compare their slopes and y-intercepts.\newlineThe slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.\newlineFor the first equation, y=−75x+710y = -\frac{7}{5}x + \frac{7}{10}, the slope (m1m_1) is −75-\frac{7}{5} and the y-intercept (b1b_1) is 710\frac{7}{10}.\newlineFor the second equation, y=43x−95y = \frac{4}{3}x - \frac{9}{5}, the slope (m2m_2) is mm00 and the y-intercept (mm11) is mm22.
  2. Calculate Slopes and Intercepts: We compare the slopes of the two lines. If the slopes are equal, the lines are either the same line (infinite solutions, consistent and dependent) or parallel (no solutions, inconsistent). If the slopes are different, the lines intersect at one point (one solution, consistent and independent).
    m1=−75m_1 = \frac{-7}{5} and m2=43m_2 = \frac{4}{3}. Since −75\frac{-7}{5} is not equal to 43\frac{4}{3}, the slopes are different.
  3. Determine Type of System: Because the slopes are different, the lines will intersect at exactly one point. This means the system of equations has one solution and is consistent and independent.

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