Question

Solving a system?

16x^2 - 3y^2 = -11
8x - y = -11


The answer for above are: (-1,3) and (-2,-5) but idk how they got that


2. x^2 +9y -10x +36y = 20
x- 3y = 2

Answer 1

Use substitution.

Answer 2

16x^2 - 3y^2 = -11
8x - y = -11

16x^2 - 3y^2 = -11
8x - y = -11 -> -y = -8x - 11 -> y = 8x + 11

16x^2 - 3y^2 = -11
y = 8x + 11

16x^2 - 3(8x + 11)^2 = -11

Continue.

Answer 3

i did do that but i didnt get the correct answer.

Answer 4

16x^2 - 3(8x + 11)^2 = -11

16x^2 - 3(8x + 11)^2 + 11 = 0

Answer 5

Did you do that also? @Srini143

Answer 6

yep!

Answer 7

thats where i get stuck

Answer 8

16x^2 - 3(8x + 11)^2 = -11

16x^2 - 3(8x + 11)^2 + 11 = 0

16x^2 - 3(8x + 11)(8x + 11) + 11 = 0

16x^2 + (-3(64x^2 + 176x + 121))+11 = 0

16x^2 + (-192x^2 - 528x - 363) + 11 = 0

-176x^2 - 528x - 363 + 11 = 0

-176x^2 - 528x - 352 = 0

Are you following?

Answer 9

yea

Answer 10

but i solved after that and i got this super long and complex answer

Answer 11

What did you get?

Answer 12

\[\left\{8 x-y=-11, y\text{=}11+8 x, y^2=64 x^2+176 x+121\right\}\]\[16 x^2-3\left(64 x^2+176 x+121\right)\text{=}-11\]\[-363-528 x-176 x^2=-11\]\[-176 x^2-528 x-352=0 \]The next surprising result was discovered using Mathematica.\[-176 (1+x) (2+x)=0\]\[{x=-1 , x=-2} \]

Answer 13

wait whattt

Answer 14

^ yup

like Rob said, you get to x values. that is what i got too.

Answer 15

Thank u sooo much!!!

Answer 16

X = -2
X = -1

Answer 17

Now you plug in and substitute those x values back into one of the equations and solve for y, to get the y values.

Answer 18

{Best Response} ?