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How many solutions does the system have? {[2y=4x+6],[y=2x+6]:} Choose 1 answer: (A) Exactly one solution (B) No solutions (C) Infinitely many solutions

How many solutions does the system have?\newline{2y=4x+6y=2x+6 \left\{\begin{array}{l} 2 y=4 x+6 \\ y=2 x+6 \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{2y=4x+6y=2x+6 \left\{\begin{array}{l} 2 y=4 x+6 \\ y=2 x+6 \end{array}\right. \newlineChoose 11 answer:\newline(A) Exactly one solution\newline(B) No solutions\newline(C) Infinitely many solutions
  1. Analyze first equation: Let's analyze the first equation:\newline2y=4x+62y = 4x + 6\newlineWe can simplify this by dividing every term by 22 to find the slope-intercept form of the equation:\newliney=2x+3y = 2x + 3
  2. Simplify equation: Now let's look at the second equation:\newliney = 22x + 66\newlineThis equation is already in slope-intercept form.
  3. Analyze second equation: We compare the slopes of the two equations:\newlineSlope of the first equation: 22\newlineSlope of the second equation: 22\newlineThe slopes are the same.
  4. Compare slopes: Next, we compare the y-intercepts of the two equations:\newliney-intercept of the first equation: 33\newliney-intercept of the second equation: 66\newlineThe y-intercepts are different.
  5. Compare y-intercepts: Since the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect.\newlineTherefore, the system of equations has no solutions.

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