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algebra

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Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
-3x + 4y = -19.5
-3x + y = -10.5

  • algebra - ,

    -3x + 4y = -19.5
    -3x + y = -10.5

    -3x + y = -10.5
    +3x +3x
    y = 3x - 10.5

    -3x +4y = -19.5

    -3x +4(3x -10.5) = -19.5
    -3x + 4(3x) + 4(-10.5) = -16.5

    -3x +12x - 42 = -16.5

    9x - 42 = -16.5
    +42 = + 42
    9x = 42 - 19.5

    9x = 22.5

    9x / 9x= 22.5 / 9
    x = 2.5

    Plug x into the original equation to solve for y
    y = 3x - 10.5

    y = 3(2.5) - 10.5
    y = 7.5 - 10.5
    y = -3

    Solution: (2.5, -3)
    Check
    -3x + 4y = -19.5 -3x + y = -10.5
    -3(2.5) + 4(-3) = - 19.5 -3(2.5) + -3 = -10.5
    -7.5 + (-12) = -19.5 -7.5 + (-3) = -10.5
    -19.5 = -19.5 -10.5 = -10.5
    True True

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