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2 years ago

Solve the following systems by substitution

Mathematics

1 answer:

Paladinen [302]2 years ago

8 0

Answer:

The answer to your question is below

Step-by-step explanation:

Question 1

x = 5 Equation l

2x + y = 10 Equation ll

- Substitute Equation l in equation ll

2(5) + y = 10

y = 10 - 10

y = 0

- Solution (5, 0)

Question 2

x + 16y = 20 Equation l

x = 4y Equation ll

Substitute equation ll in equation l

4y + 16y = 20

20y = 20

y = 20/20

y = 1

-Find x

x = 4(1)

x = 4

-Solution

(4, 1)

Question 3

2x + 8y = 20 Equation l

x = 2 Equation ll

-Substitute equation ll in equation l

2(2) + 8y = 20

4 + 8y = 20

8y = 20 - 4

8y = 16

y = 16/8

y = 2

- Solution

(2, 2)

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Find a function where f(0)=2 and f(1)=2

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Answer:

Do you want to be extremely boring?

Since the value is 2 at both 0 and 1, why not make it so the value is 2 everywhere else?

$f(x) = 2$ is a valid solution.

Want something more fun? Why not a parabola? $f(x)= ax^2+bx+c$ .

At this point you have three parameters to play with, and from the fact that $f(0)=2$ we can already fix one of them, in particular $c=2$ . At this point I would recommend picking an easy value for one of the two, let's say $a= 1$ (or even $a=-1$ , it will just flip everything upside down) and find out b accordingly: $f(1)=2 \rightarrow 1^2+b+2=2 \rightarrow b=-1$

Our function becomes

$f(x) = x^2-x+2$

Notice that it works even by switching sign in the first two terms: $f(x) = -x^2+x+2$

Want something even more creative? Try playing with a cosine tweaking it's amplitude and frequency so that it's period goes to 1 and it's amplitude gets to 2: $f(x) = A cos (kx)$

Since cosine is bound between -1 and 1, in order to reach the maximum at 2 we need $A= 2$ , and at that point the first condition is guaranteed; using the second to find k we get $2= 2 cos (k1) = cos k = 1 \rightarrow k = 2\pi$

$f(x) = 2cos(2\pi x)$

Or how about a sine wave that oscillates around 2? with a similar reasoning you get

$f(x)= 2+sin(2\pi x)$

Sky is the limit.

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Step-by-step explanation:

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