Either of these problems solved would help me a bunch



Use the substitution method to find all solutions of the system of equations

1) x^2 + y^2 = 25
y = 2x



2) x^2 + y = 9
x - y + 3 = 0

Two unknowns, two equations.

1)

Plug your second equation into the first

x^2 + (2x)^2 = 25

x^2 + 4x^2 = 25

5x^2 = 25

x^2 = 5

x = sqrt 5

or x = - sqrt 5

Same method for the second problem ( y = x + 3, then plug in this expression into the first equation), but you will need some knowledge on quadratics to solve it.

Ok thanks guys. I have a couple more.

Find the nth term of the sequence...

-1/3, 1/9, -1/27, 1/81

I don't get how to write this.


Then there is this one....

5, -25, 125, -625

Obviously it is just multiplying by -5 each time, but how would I write that. Would it just be?

a of n = n(-5)?

why dont you think about that for a second? so if we put 2 for n, you're saying a_2 = 2*-5 = -10. does that sound correct?

yes

Learn about geometric sequences :

http://en.wikipedia.org/wiki/Geometric_sequences

The number you are after is a_n(1)=5, a_n(2)=-25, a_n(3)=125

What sequence will give you this?

The answer, powers, r^n. Where r is your first term. if r = 2 starting n=1, then sequence would look like 2,4,8,16,32,..., 2^n

It also involves negatives. To get an alternating sign, you use (-1)^n, starting with a negative. But this sequence starts with a positive. so, when the term is negative, make it positive. You should know what to do here. Multiply by a negative.

(-1)(-1)^n = (-1)^(n+1)

so you have your negative sign and your power. You should be able to get a sequence now.

Get fg and I'll help.