Question

For what value of k will the system of equations 2x+2y = 5 and 3x+ky-15 = 0 has (i) a unique solution and (ii) no solution?​

Answer 1

Answer:

2x+2y=5

a1=2,b1=2,c1=5

In 3x++ky-15=0

a2=3,b2=k,c2= 15

for unique solution

a1/a2 not equal to b1/B2 = C1/c2

2/3 not equal to 2/k= 5/15

2/k=5/15

5k=30

k=30/5

k=6

hence,k=6 for unique solution

ii) for no solution

a1/a2=b1/B2 not equal to C1/c2

2/3=2/k not equal to 5/15

2/3=2/k

2k=6

k=6/2=3

hence k=3 for no solution