For a certain value of k, the system
x + y + 3z = 10
-4x + 8y + 5z = 7
kx + 2z = 3
has no solutions. What is this value of k?
What is this value of k?
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x + y + 3z = 10 | *5
-4x + 8y + 5z = 7 | *3
kx + 2z = 3
5x +5y +15z = 50
-12x+24y+15z = 21
-------------------------
17x -19y = 29 | *2
x + y + 3z = 10 | *2
kx + 2z = 3 | *3
2x + 2y +6z = 20
3kx +6z = 9
--------------------------
(2 - 3k)x + 2y = 11 | *19
(38 - 57k)x + 38y = 209
34x - 38y = 58
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(38 - 23k)x = 267 | :23
(1.652 - k)x =11.609
\(x=\dfrac{11.609}{1.652-k}\)
\(y=\frac{34x-58}{38}=\frac{\frac{34\cdot 11.609}{1.652-k}-58}{38} \)
\(y=\dfrac{10.387}{1.652-k}-1.526\)
\(z=\frac{3-kx}{2}=\frac{ 3-\frac{11.609k}{1.652-k} }{2}\)
\(z=1.5-\dfrac{5.8045k}{1.652-k}\)
\(\large k\in \mathbb R\) | -\(\infty\) < k < \(\infty\)
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