Saturday, 4 February 2017

Simple Algebra - solution

First - get rid of the images and substitute some characters that are easier to manipulate:
  1. a + b - c = 4
  2. a - 2b + 3c = -6
  3. 2a + 3b + c = 7

Add 1 + 3 together:
 a + b - c + 2a + 3b + c = 4 + 7

        4) 3a + 4b = 11

Multiply 1 by 3

3a + 3b -3c = 12
add equation 2

3a + 3b -3c +a -2b + 3c = 12 - 6
   
       5) 4a + b = 6

solve 4 & 5

3a + 4b = 11
4a +  b = 6

b = 6 - 4a

3a + 4(6 - 4a) = 11
3a + 24 - 16a = 11
-13a = -13
a = 1

3a + 4b = 11
3 + 4b = 11
4b = 8
b = 2

Substitute into 3) to get c
2a + 3b + c = 7
2 + 6 + c = 7
8 + c = 7

c = -1

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