Question

Ax + by = 12

2x + 8y = 60


In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a/b
?

Answer 1

1/4

Explanation:

If the system has infinitely many solutions, then

`\sf \boxed{\bf (a_1)/(b_1)= (a_2)/(b_2)= (c_1)/(c_2)}`

ax + by = 12 ⇒ a₁ = a ; b₁ = b ; c₁ = 12

2x + 8y =60 ⇒ a₂ = 2 ; b₂ = 8 ; c₂ = 60

`\sf (a)/(2)= (b)/(8)= (12)/(60)\\\\\\ (a)/(2)= (12)/(60)\\\\a = (12)/(60)*2\\\\a = (2)/(5)`

`\sf (b)/(8)= (12)/(60)\\\\ b = (12)/(60)*8\\\\b = (8)/(5)\\`

`\sf (a)/(b)= ( (2)/(5))/( (8)/(5))\\\\`

`\sf = (2)/(5)* (5)/(8)\\\\ = (1)/(4)`