Solve the system by elimination.(show your work)-2x + 2y + 3z = 0-2x - y + z = -32x +3y +3z = 5

Answer:x = 1 , y = 1 , z = 0Step-by-step explanation by elimination:Solve the following system: {-2 x + 2 y + 3 z = 0 | (equation 1) -2 x - y + z = -3 | (equation 2) 2 x + 3 y + 3 z = 5 | (equation 3) Subtract equation 1 from equation 2: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x - 3 y - 2 z = -3 | (equation 2) 2 x + 3 y + 3 z = 5 | (equation 3) Multiply equation 2 by -1: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+3 y + 2 z = 3 | (equation 2) 2 x + 3 y + 3 z = 5 | (equation 3) Add equation 1 to equation 3: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+3 y + 2 z = 3 | (equation 2) 0 x+5 y + 6 z = 5 | (equation 3) Swap equation 2 with equation 3: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+5 y + 6 z = 5 | (equation 2) 0 x+3 y + 2 z = 3 | (equation 3) Subtract 3/5 × (equation 2) from equation 3: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+5 y + 6 z = 5 | (equation 2) 0 x+0 y - (8 z)/5 = 0 | (equation 3) Multiply equation 3 by 5/8: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+5 y + 6 z = 5 | (equation 2) 0 x+0 y - z = 0 | (equation 3) Multiply equation 3 by -1: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+5 y + 6 z = 5 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Subtract 6 × (equation 3) from equation 2: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+5 y+0 z = 5 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Divide equation 2 by 5: {-(2 x) + 2 y + 3 z = 0 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Subtract 2 × (equation 2) from equation 1: {-(2 x) + 0 y+3 z = -2 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Subtract 3 × (equation 3) from equation 1: {-(2 x)+0 y+0 z = -2 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Divide equation 1 by -2: {x+0 y+0 z = 1 | (equation 1) 0 x+y+0 z = 1 | (equation 2) 0 x+0 y+z = 0 | (equation 3) Collect results: Answer: {x = 1 , y = 1 , z = 0