Consider the equation 6x+15=−3(ax−b), where a and b are real numbers. which values for a and b will result in the equation having an infinite number of solutions?

For infinite number of solutions , left side should equal right side

It means the value of expression on left side must be equal to the value of expression on right side.

Now here the expression is

6x+15=−3(ax−b)

Let's first simplify this, so we get...

6x+15 = -3ax +3b

Now Comparing both sides , we can compare the terms with x and the constant terms separately

So

-3a= 6 and 3b =15

first solve for a

-3a = 6

Divide both sides by -3

a=-2

Now let's solve for b

3b=15

Divide both sides by 3

b=5,

So answer is a=-2 , b=5

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