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{:[y=4.5 x+3],[y=C(x+2)]:} In the system of equations, C is a constant. For which values of C does the system have no solution? Choose 1 answer: (A) 1.5 (B) 4.5 (c) All real numbers (D) No real numbers

y=4.5x+3y=C(x+2) \begin{array}{l} y=4.5 x+3 \\ y=C(x+2) \end{array} \newlineIn the system of equations, C C is a constant. For which values of C C does the system have no solution?\newlineChoose 11 answer:\newline(A) 11.55\newline(B) 44.55\newline(C) All real numbers\newline(D) No real numbers

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Q. y=4.5x+3y=C(x+2) \begin{array}{l} y=4.5 x+3 \\ y=C(x+2) \end{array} \newlineIn the system of equations, C C is a constant. For which values of C C does the system have no solution?\newlineChoose 11 answer:\newline(A) 11.55\newline(B) 44.55\newline(C) All real numbers\newline(D) No real numbers
  1. Identify Parallel Lines: Understand when a system of equations has no solution.\newlineA system of linear equations has no solution when the lines are parallel. Parallel lines have the same slope but different yy-intercepts.
  2. Compare Slopes: Compare the slopes of the given equations.\newlineThe slope of the first equation y=4.5x+3y = 4.5x + 3 is 4.54.5.\newlineThe slope of the second equation y=C(x+2)y = C(x + 2) can be found by distributing CC to get y=Cx+2Cy = Cx + 2C.\newlineFor the lines to be parallel, the slopes must be equal, so we set the slopes equal to each other: 4.5=C4.5 = C.
  3. Solve for C: Solve for C.\newlineSince we have the equation 4.5=C4.5 = C, the value of CC that would make the lines parallel (and thus have no solution) is C=4.5C = 4.5.

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