Question

Solve:
x^2 + y^2 = 34
2x - y = 1

Answer 1

Solve the second one for Y first ;-)

Answer 2

Then plug back into the first equation, and solve for X

Answer 3

You'll then have x = something

Got back to your y= equation and substitute the now known value for X back in

Answer 4

Make sense?

Answer 5

Well sine it's y^2 wouldn't i have to do y= (1 - 2x)(1 - 2x) ?

Answer 6

Subtract 1 from both side and add +y to both sides
2x-1 = y

Answer 7

Yep, got to FOIL the binomial (2x-1)^2

Answer 8

\[(a -b)^2 = a^2 + b^2 - 2ab\]

Answer 9

@LinuxCharmd make sure you have 2x-1 though, not -2x+1 (which is the same as saying 1-2x)

Answer 10

Order matters in subtraction and division

Answer 11

So, then I would now plug 4x^2 - 4x - 1 = 0 into the y^2 to then solve for y?

Answer 12

yep! Combine like terms and solve

\[x^2 + (2x-1)^2 = 34\]
\[x^2 + 4x^2 - 4x +1 = 34\]

Answer 13

Indeed you'll have two answers for a second-order equation (aka. a quadratic), even if it's one double root or two imaginary roots (hope not).

Answer 14

So I then get -3x62 - 4x - 35 = 0 which I will take an pop in the quadratic form?

Answer 15

Sorry -3x^2 - 4x - 35. Lawl.

Answer 16

And why 2 x answers and 2 y answers?

Because that first equation you have is a circle centered at (0,0) with a radius of \(\sqrt{34}\), having a line ( y=2x-1 ) cutting across it.

The line crosses the circle's perimeter at two (x,y) coordinates. :-)

Answer 17

Got it now @LinuxCharmd ? :-)

Answer 18

I think so. That would make the answer: -2/3 +- sqrt101/3 i ?

Answer 19

Read my above post, 2 x answers, 2 y answers. Look at the awesome sketch too :D

Answer 20

See if your answers make sense

Answer 21

Hmm... I think the one I got makes sense, but I have to do something else to it, which I'm not getting.

Answer 22

Watch you order of operations on the quadratic equation:
\[x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\]
for
\[ax^2+bx+c=0\]

If it's -x\(^2\)-x-2=0 for example...
a = -1
b = -1
c = -2

Answer 23

watch your*

Answer 24

Hmm, can't find the answer. Guess I'll hunt my book up.

Answer 25

Order of operations mnemonic = PELDMAS ;-)

Answer 26

Or PELMDAS or whatever

Answer 27

It's Pemdas. Please excuse my dear aunt Sally. Parenthesis, exponents, multiplication, division, addition, subtraction. :)

Answer 28

solve it by quadratic equation

Answer 29

x^2 + y^2 = 34
2x - y = 1

y = 2x - 1

x^2 + (2x-1)^2 = 34

Now you can solve it from there

Answer 30

5x^2 - 4x - 33 = 0

Use Quadratic Formula

Answer 31

@JBrightman3

The way I remember it (operands that undo each other)

1. Parenthesis
2. Exponents & Logarithms
3. Multiplication # Division
4. Addition & Subtraction

Everybody's got their own thing, but after you've done math for long enough it become second nature. You just have to watch out for moments your neurons in your brain decide to take a nap, or a misplaced typo when typing it in isn't messing you up. That's specifically what I meant.

@Hero
Same as above, aye?

@shkak
She knows that already I believe.


^_^

Answer 32

x1=3 x2=-11/5

Answer 33

@agentx5

Well it's almost the same as mine anyways. Of course, as long as it gets us the answer, it isn't wrong. Different strokes for different folks. :)

Answer 34

Indeed!

Answer 35

I guess nobody liked my sketch :-(

Answer 36

She's gone anyways.

Answer 37

Sorry, I went to look it up in my book. I figured it out. Thanks guys!