Question

6.solve the system of equation, using determinants
x + 3y - 2 = 4
3x - 2y + 5z = - 4
5x - y - 4z = -9​

Answer 1

Step-by-step explanation:

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Sandra A. asked • 07/27/18

I want to solve this, i need help. Justify your answer please.

Consider the linear system:

x - 2y + 3z = 4

2x - 3y + az = 5

3x - 4y + 5z = b

For which values of a and b does the linear system have

a) no solution,

b) a unique solution,

c) infinitely many solutions.

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1 Expert Answer

By:

Mark M. answered • 07/27/18

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x-2y+3z = 4

2x-3y+az = 5

3x-4y+5z = b

Multiply the first equation by -2 and add to the second equation. Multiply the first equation by -3 and add to the third equation.

x - 2y + 3z = 4

y + (a-6)z = -3

2y - 4z = (b-12)

Multiply the second equation by -2 and add to the third equation:

x - 2y + 3z = 4

y + (a-6)z = -3

(-2a+8)z = (b-6)

Infinitely many solutions when -2a+8 = 0 and b-6 = 0

So, a = 4 and b = 6

No solution if -2a+8 = 0 and b-6 ≠ 0

So, a = 4 and b ≠ 6

Unique solution if a ≠ 4 and b = any real number