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There are two equations below:

 a + c = 1 ------------------ (i)

-a - 2c = 0 -----------------(ii) 

------------------------------------

     - c = 1, When I add the two equations

       c = -1 (ans) 

But my question is that If - c = 1, then how do we get c = -1? I am confuced. Please explain.

 Nov 5, 2017

Best Answer 

 #1
avatar
+1

But my question is that If - c = 1, then how do we get c = -1? I am confuced. Please explain.

 

-c=1  Multiply both sides by -1

c = -1

 

Solve the following system:
{a + c = 1 | (equation 1)
-a - 2 c = 0 | (equation 2)

Add equation 1 to equation 2:
{a + c = 1 | (equation 1)
0 a - c = 1 | (equation 2)

Multiply equation 2 by -1:
{a + c = 1 | (equation 1)
0 a+c = -1 | (equation 2)

Subtract equation 2 from equation 1:
{a+0 c = 2 | (equation 1)
0 a+c = -1 | (equation 2)

Collect results:
a = 2        and          c = -1

 Nov 5, 2017
 #1
avatar
+1
Best Answer

But my question is that If - c = 1, then how do we get c = -1? I am confuced. Please explain.

 

-c=1  Multiply both sides by -1

c = -1

 

Solve the following system:
{a + c = 1 | (equation 1)
-a - 2 c = 0 | (equation 2)

Add equation 1 to equation 2:
{a + c = 1 | (equation 1)
0 a - c = 1 | (equation 2)

Multiply equation 2 by -1:
{a + c = 1 | (equation 1)
0 a+c = -1 | (equation 2)

Subtract equation 2 from equation 1:
{a+0 c = 2 | (equation 1)
0 a+c = -1 | (equation 2)

Collect results:
a = 2        and          c = -1

Guest Nov 5, 2017
 #2
avatar+7350 
+1

Here is another way to look at it.

 

-1 * -c  =  -1 * -c        This is true since both sides are identical.

 

Since we know   -c  =  1   , we can plug in  1  for  -c , like this...

 

-1 * -c  =  -1 * 1         And simplify.

 

c  =  -1

 

Also, we can check if   c  =  -1   is a solution.

 

-c  =  1           Plug in  -1  for  c  and see if it makes the equation true.

 

-(-1)  =  1       ?

 

1  =  1            This is true, so   c  =  -1   is a solution.

 

This might seem like a lot of explanation over something simple,

but it is still good to understand I think.

 Nov 5, 2017
 #3
avatar+98125 
+1

If

 

 -c  = 1       multiply both sides by -1

 

(-1)(- c)   = (-1) 1

 

c   =    -1

 

 

 

cool cool cool

 Nov 5, 2017

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