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Question

Find the values of k for which the following system of equations have infinitely many solutions.
(i) 2x + 3y = 7
(ii) (k + 2)x + (2k + 1)y = 3(2k - 1)

A
8
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B
2
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C
4
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D
6
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Solution

The correct option is C 4
System of equations:
a1x+b1y+c1=0
a2x+b2y+c2=0
have infinite solutions if:
a1a2=b1b2=c1c2
The given system of equations will have infinitely many solutions if:
2k+2=3(2k+1)=73(2k1)2k+2=32k+1 and 3(2k+1)=73(2k1)

4k + 2 = 3k + 6 and 18k - 9 = 14k + 7
4k - 3k = 6 - 2
k = 4
Also, 18k - 9 = 14k + 7
18k - 14k = 7 + 9
4k = 16
Value of k = 4

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