Question 1011120

Solve the four equations simultaneously ,

2a+c=0
3a+2b+d=3
a+3b+c=2
b+d= -1
<pre>2a      + c         =   0 ----- eq (i)
3a + 2b        + d  =   3 ----- eq (ii)
 a + 3b + c         =   2 ----- eq (iii)
      b         + d = - 1 ----- eq (iv)

   a - 3b = - 2 ------ Subtracting eq (iii) from eq (i) -------- eq (v)
  3a +  b =   4 ------ Subtracting eq (iv) from eq (ii) -------- eq (vi)
– 3a + 9b =   6 ------ Multiplying eq (v) by – 3 ------- eq (vii)  
      10b =  10 ------ Adding eqs (vii) & (vi)
        b = {{{10/10}}}, or 1

a - 3(1) = - 2 ----- Substituting 1 for b in eq (v)
a – 3 = - 2
a = - 2 + 3, or 1

1 + d = - 1 -------- Substituting 1 for b in eq (iv)
d = - 1 – 1, or - 2

2(1) + c = 0 ------- Substituting 1 for a in eq (i)
2 + c = 0
c = - 2

{{{highlight_green(system(a = 1, b = 1, c = - 2, d = - 2))}}}