x+y+z=126x-2y+z=163x+4y+2z=28What does x, y, and z equal?

Answer:x = 20/13 , y = 16/13 , z = 120/13Step-by-step explanation:Solve the following system: {x + y + z = 12 | (equation 1) 6 x - 2 y + z = 16 | (equation 2) 3 x + 4 y + 2 z = 28 | (equation 3) Swap equation 1 with equation 2: {6 x - 2 y + z = 16 | (equation 1) x + y + z = 12 | (equation 2) 3 x + 4 y + 2 z = 28 | (equation 3) Subtract 1/6 × (equation 1) from equation 2: {6 x - 2 y + z = 16 | (equation 1) 0 x+(4 y)/3 + (5 z)/6 = 28/3 | (equation 2) 3 x + 4 y + 2 z = 28 | (equation 3) Multiply equation 2 by 6: {6 x - 2 y + z = 16 | (equation 1) 0 x+8 y + 5 z = 56 | (equation 2) 3 x + 4 y + 2 z = 28 | (equation 3) Subtract 1/2 × (equation 1) from equation 3: {6 x - 2 y + z = 16 | (equation 1) 0 x+8 y + 5 z = 56 | (equation 2) 0 x+5 y + (3 z)/2 = 20 | (equation 3) Multiply equation 3 by 2: {6 x - 2 y + z = 16 | (equation 1) 0 x+8 y + 5 z = 56 | (equation 2) 0 x+10 y + 3 z = 40 | (equation 3) Swap equation 2 with equation 3: {6 x - 2 y + z = 16 | (equation 1) 0 x+10 y + 3 z = 40 | (equation 2) 0 x+8 y + 5 z = 56 | (equation 3) Subtract 4/5 × (equation 2) from equation 3: {6 x - 2 y + z = 16 | (equation 1) 0 x+10 y + 3 z = 40 | (equation 2) 0 x+0 y+(13 z)/5 = 24 | (equation 3) Multiply equation 3 by 5: {6 x - 2 y + z = 16 | (equation 1) 0 x+10 y + 3 z = 40 | (equation 2) 0 x+0 y+13 z = 120 | (equation 3) Divide equation 3 by 13: {6 x - 2 y + z = 16 | (equation 1) 0 x+10 y + 3 z = 40 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Subtract 3 × (equation 3) from equation 2: {6 x - 2 y + z = 16 | (equation 1) 0 x+10 y+0 z = 160/13 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Divide equation 2 by 10: {6 x - 2 y + z = 16 | (equation 1) 0 x+y+0 z = 16/13 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Add 2 × (equation 2) to equation 1: {6 x + 0 y+z = 240/13 | (equation 1) 0 x+y+0 z = 16/13 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Subtract equation 3 from equation 1: {6 x+0 y+0 z = 120/13 | (equation 1) 0 x+y+0 z = 16/13 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Divide equation 1 by 6: {x+0 y+0 z = 20/13 | (equation 1) 0 x+y+0 z = 16/13 | (equation 2) 0 x+0 y+z = 120/13 | (equation 3) Collect results: Answer:  {x = 20/13 , y = 16/13 , z = 120/13