Math

2x-y=4 and 2x-y=3

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asked by Nicole
  1. We can solve this system by substitution:

    if 2x - y = 4, we can manipulate this to arrive at:

    => 2x - 4 = y

    Substitute in 2x - 4 to the second equation wherever we see a y:

    If: 2x - y = 3

    => 2x -(2x - 4) = 3
    => 2x - 2x + 4 = 3
    => 4 = 3 ... This is obviously not true.

    Thus, this system has no solution.

    If you look at the lines in a different form:

    y = 2x - 4
    y = 2x - 3

    You can see that we have two lines with the same slope: 2. They both begin at different y-intercepts: -4 and -3. Thus, they are parallel lines, and parallel lines do not intersect (meaning there is no solution to the system) unless they have the same y-intercept.

    Hope that helps =)

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