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Andru [333]
3 years ago
13

Where did the 9/4 come from?

Mathematics
2 answers:
motikmotik3 years ago
8 0

Answer:

Ok so this concept is kind of hard to explain, but basically the two equations are equal because you are adding 9/4 and then subtracting 9/4, so you just end up with 0. The reason you do that is so you can make the (x + 3/2)^2 part, which you wouldn't be able to do without the 9/4/

miss Akunina [59]3 years ago
4 0

When changing something to Vertex form you have the, in this case, coefficient to 3x which is 3 then square it. So you half it to 3/2 then square the fraction which becomes 9/4. Because you are adding the 9/4 in order to make this a perfect square you have to subtract it on the outside too leaving you with the answer provided.

In short:

When changing to stand form you need to half and square the X term to get the x intercept.

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Andreyy89

Answer:

\huge\boxed{x=-5,\ y=4\to(-5,\ 4)}

Step-by-step explanation:

\left\{\begin{array}{ccc}2x+3y=2\\5x-y=-29&\text{multiply both sides by 3}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}2x+3y=2\\15x-3y=-87\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad17x=-85\qquad\text{divide both sides by 17}\\.\qquad\dfrac{17x}{17}=\dfrac{-85}{17}\\.\qquad\boxed{x=-5}\\\\\text{Substitute it to the second equation:}\\\\5(-5)-y=-29\\\\-25-y=-29\qquad\text{add 25 to both sides}\\\\-25+25-y=-29+25\\\\-y=-4\qquad\text{change the signs}\\\\\boxed{y=4}

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