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How many solutions does the system have? {[5x-y=2],[5x-y=-2]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (c) Infinitely many solutions

How many solutions does the system have?\newline{5x−y=25x−y=−2 \left\{\begin{array}{l} 5 x-y=2 \\ 5 x-y=-2 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions

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Q. How many solutions does the system have?\newline{5x−y=25x−y=−2 \left\{\begin{array}{l} 5 x-y=2 \\ 5 x-y=-2 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze equations' structure: Analyze the structure of the equations.\newlineWe have the system of equations:\newline5x−y=25x - y = 2 ...(11)\newline5x−y=−25x - y = -2 ...(22)\newlineBoth equations have the same coefficients for xx and yy, which means they have the same slope.
  2. Compare constants on right side: Compare the constants on the right side of the equations.\newlineEquation (11) has a constant of 22, and equation (22) has a constant of −2-2.\newlineSince the constants are different, the lines represented by these equations are parallel.
  3. Determine number of solutions: Determine the number of solutions for parallel lines.\newlineParallel lines never intersect, so there are no points that satisfy both equations simultaneously.\newlineTherefore, the system of equations has 00 solutions.

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