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natita [175]
3 years ago
5

Y=2x y=-1/2x+5 system of equations

Mathematics
1 answer:
dalvyx [7]3 years ago
5 0

Answer:

<em><u>x=2, y=4</u></em> (as a point,) (2, 4)         (last part is unnecessary unless you are graphing)

Step-by-step explanation:

Use substitution.

Substitute y for 2x.

Since y=2x, you can plug 2x into the place where y goes...

Instead of y=-1/2x+5

2x=-1/2x+5....Now solve

2.5x=5 (Sorry my computer cannot type fractions very clearly)

/2.5    /2.5        (dividing by 2.5 on both sides)

<u><em>x=2</em></u>

Now just plug x into any of the equations to find y (preferably the easier one).

y=2x becomes

y=2*(2)

=4

<em><u>y=4</u></em>

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Answer:

Step-by-step explanation:

If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away.  If there is, this affects the domain.  The domain are the values in the denominator that the function covers as far as the x-values go.  If we factor both the numerator and denominator, we get this:

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Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away.  That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x.  The other factor, (x - 4), does not cancel out.  This is called a vertical asymptote and affects the domain of the function.  Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4.  That means that the function has to split at that x-value.  It comes in from the left, from negative infinity and goes down to negative infinity at x = 4.  Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity.  The domain is:

(-∞, 4) U (4, ∞)

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8 0
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Answer:

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