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Math Help - hard question

  1. #1
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    hard question

    Consider non-collinear vectors a and b. Suppose
    A=(x+4y)a+(2x+y+1)b and B=(y-2x+2)a+(2x-3y-1)b

    Find x and y such that 3A=2B
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    Consider non-collinear vectors a and b. Suppose
    A=(x+4y)a+(2x+y+1)b and B=(y-2x+2)a+(2x-3y-1)b

    Find x and y such that 3A=2B
    3A = (3x+12y)a + (6x+3y+3)b

    2B = (2y-4x+4)a + (4x-6y-2)b

    3x+12y = 2y-4x+4

    6x+3y+3 = 4x-6y-2

    solve the system for x and y
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  3. #3
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    Quote Originally Posted by skeeter View Post
    3A = (3x+12y)a + (6x+3y+3)b

    2B = (2y-4x+4)a + (4x-6y-2)b

    3x+12y = 2y-4x+4

    6x+3y+3 = 4x-6y-2

    solve the system for x and y

    i dont understand why u can set 3x+12y = 2y-4x+4 and 6x+3y+3 = 4x-6y-2
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  4. #4
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    since the 2 vectors 3A and 2B are equal, that must mean each of their respective components are equal to each other.
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