Question 1091823

Solve with elimination, explain each step given.

2a + 3b - 5c = -5 
-2a - 2b - c = -14
4a - 4b + 4c = -4
<pre>2a + 3b - 5c = - 5 -------- eq (i) 
- 2a - 2b - c = - 14 ------ eq (ii)
4a - 4b + 4c = - 4 -------- eq (iii)
b - 6c = - 19 ---------- Adding eqs (i) & (ii) ------ eq (iv)
2a - 2b + 2c = - 2 ----- Dividing eq (iii) by 2 ----- eq (v)
- 4b +   c = - 16 ------ Adding eqs (v) & (ii) ------ eq (vi)
  4b - 24c = - 76 ------ Multiplying eq (iv) by 4 --- eq (vii)
- 23c = - 92
{{{highlight_green(matrix(1,5, c, "=", (- 92)/(- 23), "=", 4))}}}

- 4b + 4 = - 16 ------- Substituting 4 for c in eq (vi)
- 4b = - 16 - 4
- 4b = - 20
{{{highlight_green(matrix(1,5, b, "=", (- 20)/(- 4), "=", 5))}}}

- 2a - 2(5) - 4 = - 14 ------- Substituting 5 for b, and 4 for c in eq (ii)
- 2a - 10 - 4 = - 14
- 2a = 0
{{{highlight_green(matrix(1,5, a, "=", 0/(- 2), "=", 0))}}}</pre>