+73 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
D) 81^2
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!!!!
+349 For the first question:
When an equation has infinitely many solutions, it usually can be reduced to 0 = 0. So, what I usually do is try to get as close as possible, like this:
\(2(x+b)=ax+c\)
\(2x+2b=ax+c\)
Well... this was as close as I got. After this, think, what value does c have to be for this equation to become 0 = 0? If you think about it, the two expressions are already very similar. a could be equal to 2, and c could be equal to 2b. To test this, substitute c for 2b to see if it leads to any contradictions:
\(2x+2b=ax+2b\)
\(2x=ax\)
\(2=a\)
This is what we assumed before, that a = 2. Therefore, c = 2b, the answer is d.
For the second question:
If you look at the expression \(x^2-4xy+4y^2\), it is a perfect square trinomial, equal to \((x-2y)^2\). Also, if you simplify \(3x-6y=9z\), it becomes \(x-2y=3z\). Substituting that into our PST, we get \((3z)^2=9z^2\). The answer is c.
