Answer:
a = 3
, b = -4
, c = 8
Step-by-step explanation:
Solve the following system:
{2 a - 3 b + 5 c = 58 | (equation 1)
-5 a + b - 4 c = -51 | (equation 2)
-6 a - 8 b + c = 22 | (equation 3)
Swap equation 1 with equation 3:
{-(6 a) - 8 b + c = 22 | (equation 1)
-(5 a) + b - 4 c = -51 | (equation 2)
2 a - 3 b + 5 c = 58 | (equation 3)
Subtract 5/6 × (equation 1) from equation 2:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+(23 b)/3 - (29 c)/6 = -208/3 | (equation 2)
2 a - 3 b + 5 c = 58 | (equation 3)
Multiply equation 2 by 6:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b - 29 c = -416 | (equation 2)
2 a - 3 b + 5 c = 58 | (equation 3)
Add 1/3 × (equation 1) to equation 3:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b - 29 c = -416 | (equation 2)
0 a - (17 b)/3 + (16 c)/3 = 196/3 | (equation 3)
Multiply equation 3 by 3:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b - 29 c = -416 | (equation 2)
0 a - 17 b + 16 c = 196 | (equation 3)
Add 17/46 × (equation 2) to equation 3:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b - 29 c = -416 | (equation 2)
0 a+0 b+(243 c)/46 = 972/23 | (equation 3)
Multiply equation 3 by 46/243:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b - 29 c = -416 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Add 29 × (equation 3) to equation 2:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+46 b+0 c = -184 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Divide equation 2 by 46:
{-(6 a) - 8 b + c = 22 | (equation 1)
0 a+b+0 c = -4 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Add 8 × (equation 2) to equation 1:
{-(6 a) + 0 b+c = -10 | (equation 1)
0 a+b+0 c = -4 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Subtract equation 3 from equation 1:
{-(6 a)+0 b+0 c = -18 | (equation 1)
0 a+b+0 c = -4 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Divide equation 1 by -6:
{a+0 b+0 c = 3 | (equation 1)
0 a+b+0 c = -4 | (equation 2)
0 a+0 b+c = 8 | (equation 3)
Collect results:
Answer: {a = 3
, b = -4
, c = 8
