Problem to solve
Solve \[4x-3y=7\], \[2x-3y+z=7\], \[4x-y+z=-8\]
Solution
STEP 1
Solve the following system:
{-3 y + 4 x = 7 | (equation 1)
2 x - 3 y + z = 7 | (equation 2)
4 x - y + z = -8 | (equation 3)
STEP 2
Subtract 1/2 × (equation 1) from equation 2:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - (3 y)/2 + z = 7/2 | (equation 2)
4 x - y + z = -8 | (equation 3)
STEP 3
Multiply equation 2 by 2:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y + 2 z = 7 | (equation 2)
4 x - y + z = -8 | (equation 3)
STEP 4
Subtract equation 1 from equation 3:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y + 2 z = 7 | (equation 2)
0 x+2 y + z = -15 | (equation 3)
STEP 5
Add 2/3 × (equation 2) to equation 3:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y + 2 z = 7 | (equation 2)
0 x+0 y+(7 z)/3 = -31/3 | (equation 3)
STEP 6
Multiply equation 3 by 3:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y + 2 z = 7 | (equation 2)
0 x+0 y+7 z = -31 | (equation 3)
STEP 7
Divide equation 3 by 7:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y + 2 z = 7 | (equation 2)
0 x+0 y+z = -31/7 | (equation 3)
STEP 8
Subtract 2 × (equation 3) from equation 2:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x - 3 y+0 z = 111/7 | (equation 2)
0 x+0 y+z = -31/7 | (equation 3)
STEP 9
Divide equation 2 by -3:
{4 x - 3 y+0 z = 7 | (equation 1)
0 x+y+0 z = -37/7 | (equation 2)
0 x+0 y+z = -31/7 | (equation 3)
STEP 10
Add 3 × (equation 2) to equation 1:
{4 x+0 y+0 z = -62/7 | (equation 1)
0 x+y+0 z = -37/7 | (equation 2)
0 x+0 y+z = -31/7 | (equation 3)
STEP 11
Divide equation 1 by 4:
{x+0 y+0 z = -31/14 | (equation 1)
0 x+y+0 z = -37/7 | (equation 2)
0 x+0 y+z = -31/7 | (equation 3)
STEP 12
Collect results:
Answer: | 
 | {x = -31/14
y = -37/7
z = -31/7