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How many solutions does the system of equations below have?\newliney=x+6y = x + 6\newliney=x+94y = x + \frac{9}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions

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Q. How many solutions does the system of equations below have?\newliney=x+6y = x + 6\newliney=x+94y = x + \frac{9}{4}\newlineChoices:\newline(A)no solution\newline(B)one solution\newline(C)infinitely many solutions
  1. Compare Equations: Compare the two equations to see if they are the same or if they intersect at a point. The equations are y=x+6y = x + 6 and y=x+94y = x + \frac{9}{4}.
  2. Compare Slopes: Since both equations are in the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept, we can compare their slopes and intercepts. The slopes (mm) of both equations are 11, which means they are parallel lines.
  3. Check Y-Intercepts: Check the y-intercepts of both equations. The first equation has a y-intercept of 66, and the second equation has a y-intercept of 94\frac{9}{4}. Since the y-intercepts are different, the lines do not intersect and are not the same line.

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