+0  
 
0
37
2
avatar

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

Guest Feb 26, 2017
Sort: 

2+0 Answers

 #1
avatar
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
avatar
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

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details