#1**+10 **

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**

Guest Nov 29, 2015

#1**+10 **

Best Answer

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**

Guest Nov 29, 2015