Mathematics

Question

I have a series of 3 questions.
I have a series of 3 questions.
I have a series of 3 questions.
I have a series of 3 questions.

1 Answer

  • 1)

    I:d+e=2
    II:d-e=4

    Isolate d in I:
    d=2-e
    substitute into II:
    II:2-e-e=4
    -2e=2
    e=-1
    substitute e into II:
    d-(-1)=4
    d+1=4
    d=3

    the solution is (3,-1)

    2)
    I:y-3x=7
    II:21+9x=3y

    Isolate y in I:
    y=7+3x
    substitute y into II:
    21+9x=3*(7+3x)
    21+9x=21+9x
    x=x

    -> Infinite amount of solutions
    note: I*3=II:
    3y-9x=21
    3y=21+9x
    so you have two identical lines

    3)

    I:5x+2y=7
    II:y=x-7

    Substitute y into I:
    5x+2*(x-7)=7
    5x+2x-14=7
    7x=-7
    x=-1

    Substitute x into II:
    y=(-1)-7
    y=-8
    so the solution is (-1,8)
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