Solve the following system: {6 t - 5 s = -4 | (equation 1) {-r - 4 s + 3 t = -4 | (equation 2) {-2 r - 4 s - 4 t = -9 | (equation 3)
Swap equation 1 with equation 3: {-(2 r) - 4 s - 4 t = -9 | (equation 1) {-r - 4 s + 3 t = -4 | (equation 2) {0 r - 5 s + 6 t = -4 | (equation 3) Subtract 1/2 × (equation 1) from equation 2: {-(2 r) - 4 s - 4 t = -9 | (equation 1) {0 r - 2 s + 5 t = 1/2 | (equation 2) {0 r - 5 s + 6 t = -4 | (equation 3) Multiply equation 1 by -1: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 2 s + 5 t = 1/2 | (equation 2) {0 r - 5 s + 6 t = -4 | (equation 3) Multiply equation 2 by 2: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 4 s + 10 t = 1 | (equation 2) {0 r - 5 s + 6 t = -4 | (equation 3) Swap equation 2 with equation 3: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 5 s + 6 t = -4 | (equation 2) {0 r - 4 s + 10 t = 1 | (equation 3) Subtract 4/5 × (equation 2) from equation 3: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 5 s + 6 t = -4 | (equation 2) {0 r+0 s+(26 t)/5 = 21/5 | (equation 3)
Multiply equation 3 by 5: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 5 s + 6 t = -4 | (equation 2) {0 r+0 s+26 t = 21 | (equation 3) Divide equation 3 by 26: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 5 s + 6 t = -4 | (equation 2) {0 r+0 s+t = 21/26 | (equation 3) Subtract 6 × (equation 3) from equation 2: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r - 5 s+0 t = (-115)/13 | (equation 2) {0 r+0 s+t = 21/26 | (equation 3) Divide equation 2 by -5: {2 r + 4 s + 4 t = 9 | (equation 1) {0 r+s+0 t = 23/13 | (equation 2) {0 r+0 s+t = 21/26 | (equation 3) Subtract 4 × (equation 2) from equation 1: {2 r + 0 s+4 t = 25/13 | (equation 1) {0 r+s+0 t = 23/13 | (equation 2) {0 r+0 s+t = 21/26 | (equation 3) Subtract 4 × (equation 3) from equation 1: {2 r+0 s+0 t = (-17)/13 | (equation 1) {0 r+s+0 t = 23/13 | (equation 2) {0 r+0 s+t = 21/26 | (equation 3) Divide equation 1 by 2: {r+0 s+0 t = (-17)/26 | (equation 1) {0 r+s+0 t = 23/13 | (equation 2) v0 r+0 s+t = 21/26 | (equation 3) Collect results:Answer: {r = -17/26 {s = 23/13 {t = 21/26
