Question

Solve the system of linear equations. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x1, x2, and x3 in terms of the parameter t.)
2x1 + x2 − 2x3 = 4
4x1 + 2x3 = 10
−4x1 + 5x2 − 17x3 = −15

Answer 1

Answer:x1 = - 2.5

x2 = 29

x3 = 10

Step-by-step explanation:

2x1 + x2 − 2x3 = 4 - - - - - - - - - - 1

4x1 + 2x3 = 10 - - - - - - - - - - - - - 2

−4x1 + 5x2 − 17x3 = −15 - - - - - - - 3

Adding equation 2 to equation 3, it becomes

5x2 - 15x3 = - 5 - - - - - - - - - - -;-4

Multiplying equation 1 by 4 and equation 3 by 2, it becomes

8x1 + 4x2 − 8x3 = 16

8x1 + 10x2 − 34x3 = −30

Subtracting

- 6x2 + 26x3 = 46- - - - - - - - - - - - 5

Multiplying equation 4 by 6 and equation 5 by 5, it becomes

30x2 - 90x3 = - 30

- 30x2 + 130x3 = 230

Adding, it becomes

20x3 = 200

x3 = 200/20 = 10

Substituting x3 = 10 into equation 4, it becomes

5x2 - 15 × 10 = - 5

5x2 - 150 = - 5

5x2 = - 5 + 150 = 145

x2 = 145/5 = 29

Substituting x3 = 10 into equation 2, it becomes

4x1 + 2 × 10 = 10

4x1 = 10 - 20 = - 10

x1 = - 10/4 = - 2.5