Solve the following system using elimination: {-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)