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

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• The numbers required are 1 and -5

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• a  + b   = - 4

2a   = 2

a   =  1

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• 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

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• a + b = −4

a − b = 6

a = 1 and b = -5

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• a = (-4 + 6)/2 = 1

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

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• 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

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• 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

2a = 2

a = 1

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

1 + b = -4

b = -5

• Steven1 month agoReport

thank you!

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• 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!

• Steven1 month agoReport

thank you!

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