for what value of k,will the following pair of equation have infinitely many solutions:2x+3y=7 and (k+2)x-3 (1-k)y =5k+1
Answer (1)
19th Mar, 2021
Given pair of equations are
2x + 3y = 7 and
(k + 2) x – 3 (1 – k) y = 5k + 1
For Infinitely many solutions,
a1/a2 = b1/b2 = c1/c2 -----------(i)
From the given equations,
a1 = 2, b1=3, c1=7
a2 = k+2, b2 = -3(1-k)
c2 = 5k+1
Thus from equation (i) we get,
2/(k+2) = 3/-3(1-k)=7/5k+1
Thus equating we get,
2/(k+2)=1/(k-1)
=> 2k-2=k+2=> k=4
For k=4 you can have infinite number of solutions.
I hope my answer helps. All the very best for your future endeavors!
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