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.

Indranil
Nov 5, 2017

#1**+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**

Guest Nov 5, 2017

#1**+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**+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.

hectictar
Nov 5, 2017