Please help:
W¹ + W² + W³ = 9 W¹ =
3W¹ + W² + 2W³ = 16 W² =
2W¹ + 3W² + 3W³ = 23 W³=
Solve the following system: a=W1, b=W2, c=W3
{a+b+c = 9 | (equation 1)
3 a+b+2 c = 16 | (equation 2)
2 a+3 b+3 c = 23 | (equation 3)
Swap equation 1 with equation 2:
{3 a+b+2 c = 16 | (equation 1)
a+b+c = 9 | (equation 2)
2 a+3 b+3 c = 23 | (equation 3)
Subtract 1/3 × (equation 1) from equation 2:
{3 a+b+2 c = 16 | (equation 1)
0 a+(2 b)/3+c/3 = 11/3 | (equation 2)
2 a+3 b+3 c = 23 | (equation 3)
Multiply equation 2 by 3:
{3 a+b+2 c = 16 | (equation 1)
0 a+2 b+c = 11 | (equation 2)
2 a+3 b+3 c = 23 | (equation 3)
Subtract 2/3 × (equation 1) from equation 3:
{3 a+b+2 c = 16 | (equation 1)
0 a+2 b+c = 11 | (equation 2)
0 a+(7 b)/3+(5 c)/3 = 37/3 | (equation 3)
Multiply equation 3 by 3:
{3 a+b+2 c = 16 | (equation 1)
0 a+2 b+c = 11 | (equation 2)
0 a+7 b+5 c = 37 | (equation 3)
Swap equation 2 with equation 3:
{3 a+b+2 c = 16 | (equation 1)
0 a+7 b+5 c = 37 | (equation 2)
0 a+2 b+c = 11 | (equation 3)
Subtract 2/7 × (equation 2) from equation 3:
{3 a+b+2 c = 16 | (equation 1)
0 a+7 b+5 c = 37 | (equation 2)
0 a+0 b-(3 c)/7 = 3/7 | (equation 3)
Multiply equation 3 by 7/3:
{3 a+b+2 c = 16 | (equation 1)
0 a+7 b+5 c = 37 | (equation 2)
0 a+0 b-c = 1 | (equation 3)
Multiply equation 3 by -1:
{3 a+b+2 c = 16 | (equation 1)
0 a+7 b+5 c = 37 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Subtract 5 × (equation 3) from equation 2:
{3 a+b+2 c = 16 | (equation 1)
0 a+7 b+0 c = 42 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Divide equation 2 by 7:
{3 a+b+2 c = 16 | (equation 1)
0 a+b+0 c = 6 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Subtract equation 2 from equation 1:
{3 a+0 b+2 c = 10 | (equation 1)
0 a+b+0 c = 6 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Subtract 2 × (equation 3) from equation 1:
{3 a+0 b+0 c = 12 | (equation 1)
0 a+b+0 c = 6 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Divide equation 1 by 3:
{a+0 b+0 c = 4 | (equation 1)
0 a+b+0 c = 6 | (equation 2)
0 a+0 b+c = -1 | (equation 3)
Collect results:
Answer: |a = 4 b = 6 c = -1
