It is given that for some real numbers a and b, the system of equations x+y=4 and (a+5)x+(b2−. 15) y=8b has infinitely many solutions for x and y. Hence, we can say that ⇒
a+5
1
=
b2−15
1
=
8b
4
This equation can be used to find the value of a, and b. Firstly, we will determine the value of b. ⇒
b2−15
1
=
8b
4
⇒b2−2b−15=0 ⇒(b−5)(b+3)=0 Hence, the values of b are 5 , and -3 , respectively. The value of a can be expressed in terms of b, which is a+5=b2−15⇒a=b2−20 When b=5,a=52−20=5 When b=−3,a=32−20=−11 The maximum value of ab=(−3)⋅(−11)=33 The correct option is A