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Which describes the system of equations below?\newliney=−2x+5y = -2x + 5\newliney=−2x+76y = -2x + \frac{7}{6}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent\newline

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Q. Which describes the system of equations below?\newliney=−2x+5y = -2x + 5\newliney=−2x+76y = -2x + \frac{7}{6}\newlineChoices:\newline(A)consistent and independent\newline(B)consistent and dependent\newline(C)inconsistent\newline
  1. Analyze slopes of equations: Analyze the slopes of both equations.\newlineEquation 11: y=−2x+5y = -2x + 5, slope = −2-2.\newlineEquation 22: y=−2x+76y = -2x + \frac{7}{6}, slope = −2-2.\newlineBoth equations have the same slope.
  2. Compare y-intercepts: Compare the y-intercepts of both equations.\newlineEquation 11: y=−2x+5y = -2x + 5, y-intercept = 55.\newlineEquation 22: y=−2x+76y = -2x + \frac{7}{6}, y-intercept = 76\frac{7}{6}.\newlineThe y-intercepts are different.
  3. Determine system type: Determine the type of system based on slopes and yy-intercepts.\newlineSince the slopes are the same but the yy-intercepts are different, the lines are parallel and never intersect.\newlineThis means the system is inconsistent.

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