Find the value of k for which the following pair of linear equations have infinitely many solutions. 2x+3y=7,(k-1)x+(k+2)y=3k.
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slope of 2x+3y = 7
m1 = -2/3
slope of (k-1)x+(k+2)y = 3k
m2 = -(k-1)/(k+2)
so, no solution means m1 = m2
-2/3 = -(k-1)/(k+2)
2/3 = (k-1)/(k+2)
2(k+2) = 3(k-1)
2k + 4 = 3k - 3
4 + 3 = 3k - 2k
k = 7
m1 = -2/3
slope of (k-1)x+(k+2)y = 3k
m2 = -(k-1)/(k+2)
so, no solution means m1 = m2
-2/3 = -(k-1)/(k+2)
2/3 = (k-1)/(k+2)
2(k+2) = 3(k-1)
2k + 4 = 3k - 3
4 + 3 = 3k - 2k
k = 7
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