2x + y + 5z = 11 22x + 6y + 8z = 5 6 x + 8y + 40z = 9
1 answer:
Solve the following system:{2 x + y + 5 z = 11 | (equation 1)22 x + 6 y + 8 z = 56 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Swap equation 1 with equation 2:{22 x + 6 y + 8 z = 56 | (equation 1)2 x + y + 5 z = 11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Subtract 1/11 × (equation 1) from equation 2:{22 x + 6 y + 8 z = 56 | (equation 1)0 x+(5 y)/11 + (47 z)/11 = 65/11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Divide equation 1 by 2:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+(5 y)/11 + (47 z)/11 = 65/11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Multiply equation 2 by 11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Subtract 1/11 × (equation 1) from equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)0 x+(85 y)/11 + (436 z)/11 = 71/11 | (equation 3)
Multiply equation 3 by 11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)0 x+85 y + 436 z = 71 | (equation 3)
Swap equation 2 with equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+5 y + 47 z = 65 | (equation 3)
Subtract 1/17 × (equation 2) from equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+(363 z)/17 = 1034/17 | (equation 3)
Multiply equation 3 by 17/11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+33 z = 94 | (equation 3)
Divide equation 3 by 33:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 436 × (equation 3) from equation 2:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y+0 z = (-38641)/33 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Divide equation 2 by 85:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+y+0 z = (-2273)/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 3 × (equation 2) from equation 1:{11 x + 0 y+4 z = 3813/55 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 4 × (equation 3) from equation 1:{11 x+0 y+0 z = 869/15 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Divide equation 1 by 11:{x+0 y+0 z = 79/15 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Collect results:Answer: {x = 79/15 y = -2273/165 z = 94/33
Please note the { are supposed to span over all equations but it interfaces doeans allow it. Please see attachment for clarification.
Swap equation 1 with equation 2:{22 x + 6 y + 8 z = 56 | (equation 1)2 x + y + 5 z = 11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Subtract 1/11 × (equation 1) from equation 2:{22 x + 6 y + 8 z = 56 | (equation 1)0 x+(5 y)/11 + (47 z)/11 = 65/11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Divide equation 1 by 2:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+(5 y)/11 + (47 z)/11 = 65/11 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Multiply equation 2 by 11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)x + 8 y + 40 z = 9 | (equation 3)
Subtract 1/11 × (equation 1) from equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)0 x+(85 y)/11 + (436 z)/11 = 71/11 | (equation 3)
Multiply equation 3 by 11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+5 y + 47 z = 65 | (equation 2)0 x+85 y + 436 z = 71 | (equation 3)
Swap equation 2 with equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+5 y + 47 z = 65 | (equation 3)
Subtract 1/17 × (equation 2) from equation 3:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+(363 z)/17 = 1034/17 | (equation 3)
Multiply equation 3 by 17/11:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+33 z = 94 | (equation 3)
Divide equation 3 by 33:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y + 436 z = 71 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 436 × (equation 3) from equation 2:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+85 y+0 z = (-38641)/33 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Divide equation 2 by 85:{11 x + 3 y + 4 z = 28 | (equation 1)0 x+y+0 z = (-2273)/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 3 × (equation 2) from equation 1:{11 x + 0 y+4 z = 3813/55 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Subtract 4 × (equation 3) from equation 1:{11 x+0 y+0 z = 869/15 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Divide equation 1 by 11:{x+0 y+0 z = 79/15 | (equation 1)0 x+y+0 z = -2273/165 | (equation 2)0 x+0 y+z = 94/33 | (equation 3)
Collect results:Answer: {x = 79/15 y = -2273/165 z = 94/33
Please note the { are supposed to span over all equations but it interfaces doeans allow it. Please see attachment for clarification.
You might be interested in