Question 1144508

I am trying to help my son with this but am lost there are no videos to help me that I can find his problem is...

3a-b-5c=22
4c=-12-a-2b
2a-19=6b+3c
<pre>There are many methods that can be used to solve for the variables. One is to SOLVE one of the equations for one of the variables. I chose to solve eq (ii) for "a"
3a - b - 5c = 22 ------ eq (i)
4c = - 12 - a - 2b______a = - 2b - 4c - 12 ------- eq (ii)
2a - 6b - 3c = 19 ------ eq (iii)

3(- 2b - 4c - 12) - b - 5c = 22 ------ Substituting - 2b - 4c - 12 for a in eq (i)
- 6b - 12c - 36 - b - 5c = 22
- 7b - 17c = 58 ------ eq (iv)
    
2(- 2b - 4c - 12) - 6b - 3c = 19 ------ Substituting - 2b - 4c - 12 for a in eq (iii)
- 4b - 8c - 24 - 6b - 3c = 19
- 10b - 11c = 43 ------ eq (v)
 
  70b + 170c = - 580 ---- Multiplying eq (iv) by - 10 ----- eq (vi)
 - 70b - 77c = 301 ------ Multiplying eq (v) by 7 --------- eq (vii)
         93c = - 279 ---- Adding eqs (vii) & (vi)
          {{{highlight_green(matrix(1,5, c, "=", (- 279)/93, "=", - 3))}}}

- 10b - 11(- 3) = 43 ------ Substituting - 3 for c in eq (v)
- 10b + 33 = 43
- 10b = 43 - 33
- 10b = 10
   {{{highlight_green(matrix(1,5, b, "=", 10/(- 10), "=", - 1))}}}

 a = - 2(- 1) - 4(- 3) - 12 ------ Substituting - 3 and 1 for c and b, respectively, in eq (ii)
 a = 2 + 12 - 12
{{{highlight_green(matrix(1,3, a, "=", 2))}}}