2x - 5y + z = 53x + 2y - 2 = 174x - 3y + 2z = 17?​

Answer:x = 17/3 , y = 1 , z = -4/3Step-by-step explanation:Solve the following system: {2 x - 5 y + z = 5 | (equation 1) -2 + 3 x + 2 y = 17 | (equation 2) 4 x - 3 y + 2 z = 17 | (equation 3) Express the system in standard form: {2 x - 5 y + z = 5 | (equation 1) 3 x + 2 y+0 z = 19 | (equation 2) 4 x - 3 y + 2 z = 17 | (equation 3) Swap equation 1 with equation 3: {4 x - 3 y + 2 z = 17 | (equation 1) 3 x + 2 y+0 z = 19 | (equation 2) 2 x - 5 y + z = 5 | (equation 3) Subtract 3/4 × (equation 1) from equation 2: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+(17 y)/4 - (3 z)/2 = 25/4 | (equation 2) 2 x - 5 y + z = 5 | (equation 3) Multiply equation 2 by 4: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 2 x - 5 y + z = 5 | (equation 3) Subtract 1/2 × (equation 1) from equation 3: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 0 x - (7 y)/2+0 z = (-7)/2 | (equation 3) Multiply equation 3 by -2/7: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 0 x+y+0 z = 1 | (equation 3) Subtract 1/17 × (equation 2) from equation 3: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 0 x+0 y+(6 z)/17 = (-8)/17 | (equation 3) Multiply equation 3 by 17/2: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 0 x+0 y+3 z = -4 | (equation 3) Divide equation 3 by 3: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y - 6 z = 25 | (equation 2) 0 x+0 y+z = (-4)/3 | (equation 3) Add 6 × (equation 3) to equation 2: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+17 y+0 z = 17 | (equation 2) 0 x+0 y+z = -4/3 | (equation 3) Divide equation 2 by 17: {4 x - 3 y + 2 z = 17 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = -4/3 | (equation 3) Add 3 × (equation 2) to equation 1: {4 x + 0 y+2 z = 20 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = -4/3 | (equation 3) Subtract 2 × (equation 3) from equation 1: {4 x+0 y+0 z = 68/3 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = -4/3 | (equation 3) Divide equation 1 by 4: {x+0 y+0 z = 17/3 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = -4/3 | (equation 3) Collect results: Answer:  {x = 17/3 , y = 1 , z = -4/3