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# In the equation above, a, b, and c are constans. If the equation has infinitely many solutions, which of the following must be equal to c?

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In the equation above, a, b, and c are constans. If the equation has infinitely many solutions, which of the following must be equal to c?

2(x+b) = ax+c

A) a

B) b

C) 2a

D) 2b

I know the answer is D but can anyone explain it? Thanks!!!!!!!!!!

AND THIS ONE!

If 3x-6y = 9z, which of the following expressions is equivalent to x^2 - 4xy + 4y^2

A) 9z

B) 3z^2

C) 9z^2

I honestly suck at theses problems with mutiple constants invovled in an equation. Does anybody have tips solving these types of problems? It will make my day. Thank YOU!!!!

Aug 8, 2018
edited by Guest  Aug 8, 2018

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2(x+b) = ax+c    Simplify

2x + 2b   = ax  + c        If this has infinite solutions, then   a  = 2  and 2b  = c

So...note that

2x  + 2b  = 2x + c     will be true for any real x whenever  2b  =  c

If 3x-6y = 9z, which of the following expressions is equivalent to x^2 - 4xy + 4y^2

Dividing the first equation through by 3, we have

x - 2y  = 3z     (1)

Notice that   x^2 - 4xy  + 4y^2   factors as     (x -2y) ( x - 2y)        (2)

So subbing  (1)  into (2)  we get     (3z) (3z)  =  9z^2   Aug 8, 2018