Question

In the system shown below, what is the sum of the x-coordinates of all solutions? pic attached

Answer 1

from the 1st equation,
3y^2 - 5x^2 = 7 ----> 3y^2 = 5x^2 + 7
now, subtitute it into the 2nd equation

Answer 2

k

Answer 3

what u get ?

Answer 4

idk how to do it, ik how to substitute but not this one

Answer 5

am i solving the second equation u wrote... the one the arrow is pointing too?

Answer 6

well, i we substitute the value of 3y^2 = 5x^2 + 7 to 3y^2-x^2=23, gives
5x^2 + 7- x^2=23, right ?

Answer 7

*if

Answer 8

right

Answer 9

then, just simplify it, what u get ?

Answer 10

5x^2 - x^2=16

Answer 11

or 4x^2=16

Answer 12

or 4x^2 - 16 = 0, right ?

Answer 13

yes

Answer 14

x=-2 and x=2??

Answer 15

ok now without to find the roots, we can determine the sum of roots of equation kuadratic :
ax^2-bx+c=0,
just use formula x1 + x2 = -b/a

Answer 16

which u get what once there plugged in?

Answer 17

x1+x2=o/4?

Answer 18

ax^2+bx+c=0... (sorry, trouble my keyboard)
yes.. 0/4 = 0

Answer 19

so the sum of all x coordinates is 0?

Answer 20

yeps...
another way, from ur solution : x1=-2 and x2=2
so, x1+x2 = -2 + 2 = 0

Answer 21

thankyou

Answer 22

welcome