Can someone help me with this ques5ion

Question

Determine the values of

a

and

b

such that the following system of linear equations has infinitely many

solutions.

ax + 3y + b = 0

4x + 5y − 12 = 0

Answer 1

the y coefficient of the 1st equation is 3/5 that of the 2nd equation, so the same ratio is needed for the x coefficient and the constant term

a/4 =3/5 = b/-12

a=12/5 and b=-36/5

that makes the 2 equations linearly dependent with an infinite number of solutions They're the same line graphically.