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solve each system

1) 3x + y = 6
2x + 3y = 13

2) 2x + 5y - 6 = 0
-2x + y - 2 = 0

3) x + 3y = 6
4x - 5y = 7

  • Math -

    I'll solve the first one, leaving you a chance to practice with the rest.
    3x + y = 6 .....(1)
    2x + 3y = 13 ....(2)

    Multiply (1) by 3 and subtract (2) to eliminate y:

    9x + 3y = 18 .....(1a)
    2x + 3y = 13 .....(2a)
    Subtract:
    7x = 5
    x=5/7 .....(3)
    Substitute (3) in 1
    3(5/7) + y = 6
    y = 6-15/7
    =27/7 ....(4)
    Substitute (3) and (4) in (2) to check:
    2(5/7) + 3(27/7)
    =(10+81)/7
    =13 OK.

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