Question

Solve the system below and identify the shape of the graph of the equation.

7y^2+x^2=64
x+y=4

Answer 1

x = - y + 4
substitute, it's a long process doing this stuff lol.
You can tell the first one is a circle from its form
and the second equation is a line.

Answer 2

The first one is close to a circle but not exactly.

Answer 3

what do i do with x = -y+4

Answer 4

Substitute it into the other equation for x.
\[\huge 7y^2 + (4-y)^2 = 64\]
and solve for y.

Answer 5

and then find the y (factor y)

Answer 6

first would I multiply (4-y)(4-y)??

Answer 7

yeah

Answer 8

I got 16+y^2, is that correct?

Answer 9

16 + y^2 - 8y

Answer 10

oh! I thought one was positive and one was negative!

Answer 11

(4-y)^2 = (4-y)(4-y)

Answer 12

so after i get that solution what do i plug it into?

Answer 13

\[\huge 7y^2 + 16 + y^2 - 8y = 64\]
get everything on one side and combine the like terms and then use the quadratic formula or factor it. to get your y values.

Answer 14

if u confuse, try using this formula :
\[\frac{ (-b)\pm \sqrt{b ^{2}-4ac} }{ 2a }\]

Answer 15

thanks! let me solve first using what shamil gave me :)

Answer 16

okay I got 1+- 40/2 which gave me 41/2 and -39/2. is that correct? i used the quadratic formula

Answer 17

did i do this write though if the question says "For questions 10 - 11, solve each system. In your work, identify the shape of the graph of each equation." ??

Answer 18

7y^2 +16 + y^2 - 8y = 64
8y^2 - 8y - 48 = 0
8(y^2 - y - 6 ) = 0
y^2 -y - 6 = 0
(y-2)(y+3) = 0
y = 2, y = -3

Answer 19

How did you end up with those values? o_O

Answer 20

tblue said to use quadratic formula ._. so no?

Answer 21

it just another way

Answer 22

(y-3) ( y+2) = 0
oops

Answer 23

y = 3, y = -2 *

Answer 24

i like using factoring where possible it's much easier.

Answer 25

hm, what would i do with those numbers then?

Answer 26

so u can substitute to x + y = 4

Answer 27

So anyways.
y = 3, y = -2
x+y=4
x + 3 =4
x = 1,
x -2 =4
x =6

Answer 28

So, your solutions are (1,3) and ( 6,-2)

Answer 29

he's right

Answer 30

thank you! so @shamil98 (1,3) and (6,-2) would be the equation to each system?

Answer 31

Those are the solutions to the system.

Answer 32

& when it says " identify the shape of the graph of each equation" that would be where you said the top eqation was close to being a circle and the bottom equation was a line?