Q:

Solution for: -x + 3y -2z = 192x + y - z = 5-3x - y + 2z = -7

Accepted Solution

A:
Answer:x = -1 , y = 4 , z = -3Step-by-step explanation:Solve the following system: {-x + 3 y - 2 z = 19 | (equation 1) 2 x + y - z = 5 | (equation 2) -3 x - y + 2 z = -7 | (equation 3) Swap equation 1 with equation 3: {-(3 x) - y + 2 z = -7 | (equation 1) 2 x + y - z = 5 | (equation 2) -x + 3 y - 2 z = 19 | (equation 3) Add 2/3 × (equation 1) to equation 2: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+y/3 + z/3 = 1/3 | (equation 2) -x + 3 y - 2 z = 19 | (equation 3) Multiply equation 2 by 3: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+y + z = 1 | (equation 2) -x + 3 y - 2 z = 19 | (equation 3) Subtract 1/3 × (equation 1) from equation 3: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+y + z = 1 | (equation 2) 0 x+(10 y)/3 - (8 z)/3 = 64/3 | (equation 3) Multiply equation 3 by 3/2: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+y + z = 1 | (equation 2) 0 x+5 y - 4 z = 32 | (equation 3) Swap equation 2 with equation 3: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+5 y - 4 z = 32 | (equation 2) 0 x+y + z = 1 | (equation 3) Subtract 1/5 × (equation 2) from equation 3: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+5 y - 4 z = 32 | (equation 2) 0 x+0 y+(9 z)/5 = (-27)/5 | (equation 3) Multiply equation 3 by 5/9: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+5 y - 4 z = 32 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Add 4 × (equation 3) to equation 2: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+5 y+0 z = 20 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Divide equation 2 by 5: {-(3 x) - y + 2 z = -7 | (equation 1) 0 x+y+0 z = 4 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Add equation 2 to equation 1: {-(3 x) + 0 y+2 z = -3 | (equation 1) 0 x+y+0 z = 4 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Subtract 2 × (equation 3) from equation 1: {-(3 x)+0 y+0 z = 3 | (equation 1) 0 x+y+0 z = 4 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Divide equation 1 by -3: {x+0 y+0 z = -1 | (equation 1) 0 x+y+0 z = 4 | (equation 2) 0 x+0 y+z = -3 | (equation 3) Collect results: Answer:  {x = -1 , y = 4 , z = -3