bellaself52713
Answered

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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
?

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 Ab class=

Sagot :

songpainter23

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.

devishri1977

Answer:

1/4

Step-by-step explanation:

If the system has infinitely many solutions, then

     [tex]\sf \boxed{\bf \dfrac{a_1}{b_1}= \dfrac{a_2}{b_2}= \dfrac{c_1}{c_2}}[/tex]

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

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

[tex]\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}[/tex]

                         [tex]\sf \dfrac{b}{8}= \dfrac{12}{60}\\\\ b = \dfrac{12}{60}*8\\\\b = \dfrac{8}{5}\\[/tex]

[tex]\sf \dfrac{a}{b}= \dfrac{ \dfrac{2}{5}}{ \dfrac{8}{5}}\\\\[/tex]

    [tex]\sf = \dfrac{2}{5}* \dfrac{5}{8}\\\\ = \dfrac{1}{4}[/tex]

     

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