A number besides 0. That both multiplied by 0.5 and added to 0.5 gives the same result

Guest Feb 26, 2017

#1**0 **

A number besides 0. That both multiplied by 0.5 and added to 0.5 gives the same result

a x 1/2 =b

a + 1/2 =b

Solve the following system:

{a/2 = b | (equation 1)

a + 1/2 = b | (equation 2)

Express the system in standard form:

{a/2 - b = 0 | (equation 1)

a - b = -1/2 | (equation 2)

Swap equation 1 with equation 2:

{a - b = (-1)/2 | (equation 1)

a/2 - b = 0 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{a - b = -1/2 | (equation 1)

0 a - b/2 = 1/4 | (equation 2)

Multiply equation 1 by 2:

{2 a - 2 b = -1 | (equation 1)

0 a - b/2 = 1/4 | (equation 2)

Multiply equation 2 by 4:

{2 a - 2 b = -1 | (equation 1)

0 a - 2 b = 1 | (equation 2)

Divide equation 2 by -2:

{2 a - 2 b = -1 | (equation 1)

0 a+b = (-1)/2 | (equation 2)

Add 2 × (equation 2) to equation 1:

{2 a+0 b = -2 | (equation 1)

0 a+b = -1/2 | (equation 2)

Divide equation 1 by 2:

{a+0 b = -1 | (equation 1)

0 a+b = -1/2 | (equation 2)

Collect results:

**Answer: |a = -1 and b= -1/2**

Guest Feb 26, 2017

#2**0 **

a x 1/2 =b..........(1)

a + 1/2 =b..........(2)

From 2 above we have:

a = b - 1/2, we sub into (1)

(b -1/2) x 1/2 =b

1/2b - 1/4 = b

- 1/4 = b - 1/2b

- 1/4 = 1/2b divide both sides by 1/2

b = - 1/4 x 2

**b = - 1/2** sub into (2) above and we have:

a + 1/2 = - 1/2

a = -1/2 - 1/2

**a = - 1**

Guest Feb 26, 2017