Need some Geometry help...?

Question

Two things. I need to know how to:

"Solve each system of linear equations. You may solve by either substitution or linear combination."

and the question is

3b + 2a = 2

-2b + a = 8

and the other question was

"Solve by factoring."

X^2 - 20x + 75 = 0

I need step-by-step help, because I really don't get it...

Thanks.

Answer 1

http://www.youtube.com/user/khanacademy

Here you go,

this guy has everything

you need.

Answer 2

for the first one, you can graph the equations and find where they intersect.

to explain the second one is kinda hard, but you find numbers that multiply to equal 75 and add to 20, which is -5 and -15

so the answer to that is (x - 5)(x - 15)

Answer 3

3b + 2a = 2

-2b + a = 8

I'll solve this problem using substitution, so first, change one of the equations to a = ______ or b = ______.

I'm going to use the second equation to make a = _____

-2b + a = 8

a = 2b + 8

Now that I know a = 2b + 8, I'm going to substitute 2b + 8 for a in the first equation like this:

3b + 2a = 2

3b + 2(2b+8) = 2

Now solve for b.

3b + 2(2b+8) = 2

3b + 4b + 16 = 2

7b + 16 = 2

7b = -14

b = -2

Now that you know that b = -2, you can substitute -2 for b in either of the two equations in the system in order to find a. I'll substitute using the first equation.

3b + 2a = 2

3(-2) + 2a = 2

-6 + 2a = 2

2a = 8

a = 4

ANSWER: a = 4, b = -2

x^2 - 20x + 75 = 0

This one is more like guess-and-check. Basically, you need to find two numbers that multiply to get you 75 and add to get -20. That's the simplest I can put it for you.

So... two numbers that multiply to get 75 and add to get -20 are.. *thinks*.. -15 and -5.

So now you set up the equation like this:

(x-15)(x-5) = 0

x - 15 = 0    OR    x - 5 = 0

x = 15     OR    x = 5

ANSWER: x = 15 or 5

Sorry, it's really hard to explain this problem by typing it out. I think you should try looking online and search "solving quadratic equations". It should explain it better than I did.

Answer 4

for the first one use substitution

3b+2a=2

-2b+a=8

what you do to one side you have to do to the other

-2+a=8

a=8+2b    ad 2b to both sides

3b+2(8+2b)=2 substitute a

3b+16+4b=2 add 3b+4b

7b+16=2subtract 16

7b=-14 divide by 7

b=-2

-2(-2)+a=8 substitute b to find a

4+a=8 subtract 4

a=4

double check your answer

-2(-2)+4=8

4+4=8

8=8

Answer 5

a=4

b=-2

solve one of the eq. for one of the leters.

eg: 3b+2a=2    a=(2-3b)/2

then plug a into the other eq.

then solve for b

after substitute b into the other eq again

Answer 6

Ok this is NOT geometry...but I can do this ( its algebra 1) . You need to multiply the top and bottom eq.'s with a number that u can used to cancel either the a;s or the b's, for the a's multiply the bottom only with a negative TWO and then solve for b. Make sure to solve for both a and b the same way and then you can get the point in which they intersect. Or u can graph it.

For the second thingy....u need two numbers that multiply to  make 150 ( you get this my multiply 2 and 75) and then those same numbers need to add up to a negative 20 (middle number)

I kno how to do this...I just suck at explaining online, but I hope i helped =)

Answer 7

Sorry I ended up with a b in geometry last year but my test grade was.....bad.

Answer 8

I hate geometry like every one else but it took it last year in honors and did okay

substitution

3b+2a=2

-2b+a=8

choice an equation

-2b+a=8 is easier

know -2b+a=8

        +2b     +2b

a=2b+8

know substitute into the first equation

3b+2(2b+8)=2

3b+4b+16=2

7b+16=2

    -16  -16

7b =-14

/7    /7

equals

b=-2

know but b into a problem to find a

3(-2)+2a=2

-6+2a=2

+6      +6

2a=-8

a=4

check

3(-2)+2(4)

-6+8=2!

second problem means which factors of 75 added together get u 20

its really complicated email me for more but the answer is (x-15)(x-5) that how u write it meaning x=15 or 5

check with foil (mutiple all the elements in order of)

First

Outer

Inner

Last

x^2-5x-15x+75

x^2-20x+75!

Answer 9

I wasn't paying attention during linear equations...oops :]

As for the second one

x^2 - 29x + 75 = 0

Step 1: Whenever a standard algebraic equation like this has a 0 at the end and a number with no variable on the other side of the equal sign, your first instinct is to get that number on the side with the zero.

x^2 -29x = -75

Step 2: x^2 means x to the second power. x times x is 2 x. Simple enough. So now just combine those. Negative 2 minus 29 is negative 27.

2x -29x

-27x = -75

Step 3: At this point, you have a single value on both sides of the equal sign. One thing that confused a lot of people is that both are negative. When both are negative, you can actually just consider both to be positive. Why? Because if you want to switch their sides, they would both be positive. A negative times a negative is a positive, anyways.

So all you have to do now is simplify.

-27x = -75

(27x = 75)

x = 2.7777778