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

Answer:
There is no value of a/b because the system has infinitely many solutions.

Step-by-step explanation:

We know that there is no solution because, when we solve for x and y, we get x = 12 and y = -6. This means that there are infinitely many solutions because we can plug in any value for a and b and still get a correct answer.

Answer 2

Answer:

1/4

Step-by-step explanation:

If the system has infinitely many solutions, then

     $\sf \boxed{\bf \dfrac{a_1}{b_1}= \dfrac{a_2}{b_2}= \dfrac{c_1}{c_2}}$

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

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

$\sf \dfrac{a}{2}= \dfrac{b}{8}= \dfrac{12}{60}\\\\\\ \dfrac{a}{2}= \dfrac{12}{60}\\\\a = \dfrac{12}{60}*2\\\\a = \dfrac{2}{5}$

                         $\sf \dfrac{b}{8}= \dfrac{12}{60}\\\\ b = \dfrac{12}{60}*8\\\\b = \dfrac{8}{5}$

$\sf \dfrac{a}{b}= \dfrac{ \dfrac{2}{5}}{ \dfrac{8}{5}}$

    $\sf = \dfrac{2}{5}* \dfrac{5}{8}\\\\ = \dfrac{1}{4}$