Algebra

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How many solutions does this system of equations have?

y = 4x + 3 and 2y - 8x = 3

One, two, infinitely many, or no solutions? My answer is no solutions.

  • Algebra -

    y = 4 x + 3
    y = 4 x + 3/2

    two lines with the same slope but different y axis intercepts. They never cross each other and therefore there is no solution to this problem.

  • Algebra -

    Thanks. I have a couple more:

    x = -4y + 4 and 2x + 8y = 8

    Answer: Infinitely many solutions

    x - 3y = 15 and 3x - 9y = 4

    Answer: Infinitely many solutions

    y - 5x = -6 and 3y - 15x = -12

    Answer: One solution

  • Algebra -

    x - 3y = 15 and 3x - 9y = 4
    x - 3 y = 4/3
    Same slope, never cross NO solutions !

    Answer: Infinitely many solutions DIASAGREE

    y - 5x = -6 and 3y - 15x = -12
    y - 5 x = -4
    AGAIN, they are NOT the same. They are PARALLEL and never cross NO solutions
    same m = slope = either the same (infinite solutions of parallel (different y intercept) which means ZERO solutions

    Answer: One solution NO!

  • Algebra -

    Seems like both have no solutions. I went a bit off in my calculation. I see now.

  • Algebra -

    When in doubt, sketch a graph

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