Problem to solve
Solve \[-10x+3y+z=-2\], \[3x-2y+5z=4\], \[-6x+4y+2z=1\]
Solution
STEP 1
Solve the following system:
{-10 x + 3 y + z = -2 | (equation 1)
3 x - 2 y + 5 z = 4 | (equation 2)
-6 x + 4 y + 2 z = 1 | (equation 3)
STEP 2
Add 3/10 × (equation 1) to equation 2:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - (11 y)/10 + (53 z)/10 = 17/5 | (equation 2)
-(6 x) + 4 y + 2 z = 1 | (equation 3)
STEP 3
Multiply equation 2 by 10:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
-(6 x) + 4 y + 2 z = 1 | (equation 3)
STEP 4
Subtract 3/5 × (equation 1) from equation 3:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
0 x+(11 y)/5 + (7 z)/5 = 11/5 | (equation 3)
STEP 5
Multiply equation 3 by 5:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
0 x+11 y + 7 z = 11 | (equation 3)
STEP 6
Add equation 2 to equation 3:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
0 x+0 y+60 z = 45 | (equation 3)
STEP 7
Divide equation 3 by 15:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
0 x+0 y+4 z = 3 | (equation 3)
STEP 8
Divide equation 3 by 4:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y + 53 z = 34 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 9
Subtract 53 × (equation 3) from equation 2:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x - 11 y+0 z = -23/4 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 10
Divide equation 2 by -11:
{-(10 x) + 3 y + z = -2 | (equation 1)
0 x+y+0 z = 23/44 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 11
Subtract 3 × (equation 2) from equation 1:
{-(10 x) + 0 y+z = -157/44 | (equation 1)
0 x+y+0 z = 23/44 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 12
Subtract equation 3 from equation 1:
{-(10 x)+0 y+0 z = -95/22 | (equation 1)
0 x+y+0 z = 23/44 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 13
Divide equation 1 by -10:
{x+0 y+0 z = 19/44 | (equation 1)
0 x+y+0 z = 23/44 | (equation 2)
0 x+0 y+z = 3/4 | (equation 3)
STEP 14
Collect results:
Answer: | 
 | {x = 19/44
y = 23/44
z = 3/4