Question

Solve:

x^2 +2y^2 =33
3x +2y = -11

The answer is suppose to be: ( -5,2) and (-1,-4) but idk how they got that! :(

Answer 1

helllppp! ;o

Answer 2

Do you recognize what those formulas are?

Answer 3

yeah they are for Conic solutions. and they are inequalities right?

Answer 4

The first one is an ellipse, the second one is a line.

Answer 5

Oh yeah that i know.

Answer 6

the solutions are the points where the line crosses the ellipse.

Answer 7

Yeha, i know how to do it by graphing but I need to know how to solve it by using equations etc

Answer 8

Right, I'm just making sure you understand the setup.

Here's how you can solve it exactly:

Take the second equation and solve it for one of the variables. Say you solve it for \(x\): now you replace \(x\) in the first equation with whatever you got when you solved the second equation for \(x\), which will give you an equation in terms of \(y\). Solve that for \(y\) — it will be a quadratic and give you two solutions. Plug those two values of \(y\) into either original equation to find the corresponding values of \(x\).

Answer 9

Okay i did everytihng up till hte quadratic part but its not factorable . so i dont know how to get the 2 answers.

Answer 10

what do you get for a quadratic?

Answer 11

i got till this point and then get confused. x^2 +2 (.5(-11-3x))^2 = 33

Answer 12

because i get like decimal points after this and no whole numbers

Answer 13

You solved for \(y\) and got \(y = \frac{1}{2}(-11-3x)\)
Generally better to avoid using decimals when doing algebra...

\[x^2 + 2(\frac{1}{2}(-11-3x))^2 = 33\]Now we just carefully expand that
\[x^2+2*(\frac{1}{2})^2(-11-3x)^2 =33\]\[x^2+\frac{1}{2}((-11)^2+33x+33x+9x^2) = 33\]
Try it from there...

Answer 14

Might be convenient to multiply everything by 2 to get rid of that fraction...

Answer 15

and then divide everything by 11 once you've done that

Answer 16

I think you'll find that you can factor the result.

Answer 17

i got
10x^2+66x+88

Answer 18

is that right?

Answer 19

No, that's not correct. for starters, it isn't an equation.

Answer 20

aww what did i do wrong?

Answer 21

I'm not sure, you didn't show me your work...

Answer 22

x^2 +.5 (121+33x+33x+9x^2) = 33
10x^2+66x+88=0

Answer 23

what did I say about using decimals while doing algebra? By doing that instead of writing a fraction, you completely missed it when you expanded :-(

\[x^2+\frac{1}{2}((-11)^2+33x+33x+9x^2) = 33\]Multiply by 2:
\[2x^2 + 2*\frac{1}{2}((-11)^2+33x+33x+9x^2) = 2*33\]\[2x^2+(121+66x+9x^2) = 66\]

Answer 24

collect like terms, divide out any common factors, then factor for the solution...

Answer 25

AHHH ur the best! thank you!

Answer 26

i got it!

Answer 27

Great!