Solve the following System of Equations5x+4y-z=12x-2y+z=1-x-y+z=2

Answer:x = 0 , y = 1 , z = 3Step-by-step explanation:Solve the following system: {5 x + 4 y - z = 1 | (equation 1) 2 x - 2 y + z = 1 | (equation 2) -x - y + z = 2 | (equation 3) Subtract 2/5 × (equation 1) from equation 2: {5 x + 4 y - z = 1 | (equation 1) 0 x - (18 y)/5 + (7 z)/5 = 3/5 | (equation 2) -x - y + z = 2 | (equation 3) Multiply equation 2 by 5: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y + 7 z = 3 | (equation 2) -x - y + z = 2 | (equation 3) Add 1/5 × (equation 1) to equation 3: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y + 7 z = 3 | (equation 2) 0 x - y/5 + (4 z)/5 = 11/5 | (equation 3) Multiply equation 3 by 5: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y + 7 z = 3 | (equation 2) 0 x - y + 4 z = 11 | (equation 3) Subtract 1/18 × (equation 2) from equation 3: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y + 7 z = 3 | (equation 2) 0 x+0 y+(65 z)/18 = 65/6 | (equation 3) Multiply equation 3 by 18/65: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y + 7 z = 3 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Subtract 7 × (equation 3) from equation 2: {5 x + 4 y - z = 1 | (equation 1) 0 x - 18 y+0 z = -18 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Divide equation 2 by -18: {5 x + 4 y - z = 1 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Subtract 4 × (equation 2) from equation 1: {5 x + 0 y - z = -3 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Add equation 3 to equation 1: {5 x+0 y+0 z = 0 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Divide equation 1 by 5: {x+0 y+0 z = 0 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 3 | (equation 3) Collect results: Answer: {x = 0 , y = 1 , z = 3