How do i solve equations by substitution?

1 answer:

4 0

Just doing one! Here's my problem: x-y-11 x-3y=1

So when you subsitute everything it should look like this: 1y-11-3y=1 (There needs to be a one in front of the y because it's just always been there. they don't always put it in the eqation.) You need to + the 11 and you have to do that to each side. So... 1y-11-3=1
+11 +11
Now it should look like this: 1y-3y=12
Combine the 1y and -3y to get -4y=12 Last step is divide -4y and 12 by 4 . Answer is y=3

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Show all work to identify the asymptotes and state the end behavior of the function f(x)=5x/x-25

Nina [5.8K]

Using the asymptote concept, it is found that:

The vertical asymptote is of x = 25.

The horizontal asymptote is of y = 5.

Considering the horizontal asymptote, it is found that the end behavior of the function is that it tends to y = 5 to the left and to the right of the graph.

<h3>What are the asymptotes of a function f(x)?</h3>

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

$f(x) = \frac{5x}{x - 25}$

Considering the denominator, the vertical asymptote is:

x - 25 = 0 -> x = 25.

The horizontal asymptote is found as follows:

$y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = \lim_{x \rightarrow \infty} 5 = 5$