Solve the following system:
{2 x+y+3 z = -9 | (equation 1)
4 x+2 y+5 z = -7 | (equation 2)
-5 x-6 y-z = -1 | (equation 3)
Swap equation 1 with equation 3:
{-(5 x)-6 y-z = -1 | (equation 1)
4 x+2 y+5 z = -7 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Add 4/5 × (equation 1) to equation 2:
{-(5 x)-6 y-z = -1 | (equation 1)
0 x-(14 y)/5+(21 z)/5 = (-39)/5 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Multiply equation 1 by -1:
{5 x+6 y+z = 1 | (equation 1)
0 x-(14 y)/5+(21 z)/5 = -39/5 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Multiply equation 2 by 5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Subtract 2/5 × (equation 1) from equation 3:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x-(7 y)/5+(13 z)/5 = (-47)/5 | (equation 3)
Multiply equation 3 by 5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x-7 y+13 z = -47 | (equation 3)
Subtract 1/2 × (equation 2) from equation 3:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x+0 y+(5 z)/2 = (-55)/2 | (equation 3)
Multiply equation 3 by 2/5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract 21 × (equation 3) from equation 2:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+0 z = 192 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Divide equation 2 by -14:
{5 x+6 y+z = 1 | (equation 1)
0 x+y+0 z = (-96)/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract 6 × (equation 2) from equation 1:
{5 x+0 y+z = 583/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract equation 3 from equation 1:
{5 x+0 y+0 z = 660/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Divide equation 1 by 5:
{x+0 y+0 z = 132/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Collect results:
Answer: | {x = 132/7 y = -96/7 z = -11
Solve the following system:
{2 x+y+3 z = -9 | (equation 1)
4 x+2 y+5 z = -7 | (equation 2)
-5 x-6 y-z = -1 | (equation 3)
Swap equation 1 with equation 3:
{-(5 x)-6 y-z = -1 | (equation 1)
4 x+2 y+5 z = -7 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Add 4/5 × (equation 1) to equation 2:
{-(5 x)-6 y-z = -1 | (equation 1)
0 x-(14 y)/5+(21 z)/5 = (-39)/5 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Multiply equation 1 by -1:
{5 x+6 y+z = 1 | (equation 1)
0 x-(14 y)/5+(21 z)/5 = -39/5 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Multiply equation 2 by 5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
2 x+y+3 z = -9 | (equation 3)
Subtract 2/5 × (equation 1) from equation 3:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x-(7 y)/5+(13 z)/5 = (-47)/5 | (equation 3)
Multiply equation 3 by 5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x-7 y+13 z = -47 | (equation 3)
Subtract 1/2 × (equation 2) from equation 3:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x+0 y+(5 z)/2 = (-55)/2 | (equation 3)
Multiply equation 3 by 2/5:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+21 z = -39 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract 21 × (equation 3) from equation 2:
{5 x+6 y+z = 1 | (equation 1)
0 x-14 y+0 z = 192 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Divide equation 2 by -14:
{5 x+6 y+z = 1 | (equation 1)
0 x+y+0 z = (-96)/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract 6 × (equation 2) from equation 1:
{5 x+0 y+z = 583/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Subtract equation 3 from equation 1:
{5 x+0 y+0 z = 660/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Divide equation 1 by 5:
{x+0 y+0 z = 132/7 | (equation 1)
0 x+y+0 z = -96/7 | (equation 2)
0 x+0 y+z = -11 | (equation 3)
Collect results:
Answer: | {x = 132/7 y = -96/7 z = -11
