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
Sandra A.
I really appreciate your support. Thanks a lot.
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07/27/18
Sandra A.
07/27/18