Find two numbers a and b whose sum a+b is -4 and whose difference a−b is 6?

8 Answers

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  • David
    Lv 7
    1 year ago

    The numbers required are 1 and -5

  • Como
    Lv 7
    1 year ago

    a  + b   = - 4

    a -  b   = 6_______add

    2a   = 2

    a   =  1

  • Anonymous
    1 year ago

    It's simultaneous equation.

    (i) a + b = -4

    (ii) a - b = 6

    Add (i) and (ii) which will illiminate b

    (iii) 2a = 2

    (iv) a = 1

    Substitute (iv) into either (i) or (ii)

    (v) 1 + b = -4

    (vi) b = -5____________________or(i) a + b = -4(ii) a - b = 6or(iii) a = b + 6Substitute (iii) into (i)(iv) b + 6 + b = -4(v) 2b = -10(vi) b = -5Substitute (vi) into (i)(vii) a -5 = -4(viii) a = 1

  • 1 year ago

    a + b = −4

    a − b = 6

    a = 1 and b = -5

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  • 1 year ago

    a = (-4 + 6)/2 = 1

    b = (-4 - 6)/2 = -5

  • geezer
    Lv 7
    1 year ago

    A + B = -4

    A - B = 6

    Just combine the two equations, giving you :

    A + A + B - B = 6 - 4

    2A = 2

    A = 1

    and B = -5 .. because 1 + -5 = -4 and 1 - -5 = 6

  • 1 year ago

    The average is -4/2 = -2.

    The difference is 6, so the differences from the average must be half that, or ±3.

    Therefore the numbers are

    -2-3 = -5

    -2+3 = +1

    But the way they want you to do it is to solve the two equations:

    a + b = -4

    a - b = 6

    Add those to get

    2a = 2

    a = 1

    Then use either equation to find b, e.g.,

    1 + b = -4

    b = -5

  • Pyrus
    Lv 6
    1 year ago

    a+b = -4

    a-b = 6

    We sum the two equations up, and we get

    a + a + b - b = - 4 + 6

    2a = 2

    a = 1

    Now, to find b, just replace in one of the equations:

    1 + b = -4

    b = -5

    Let's make sure:

    a + b = -4 (let's replace)

    1 - 5 = -4 (correct)

    a - b = 6

    1 - (-5) = 6

    1 + 5 = 6 (correct).

    DONE!

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