Question

What are the x-coordinates of the solutions to this system of equations?
x2 + y2 = 100
y = x + 2
Select one:
a. 2 and 10
b. 10 and -2
c. 6 and -8
d. 6 and 8

Answer 1

Do you know how to start?

Answer 2

no.

Answer 3

y = x + 2
Substitute above for y in x^2 + y^2 = 100. Simplify.
You will get a quadratic equation in x. Solve for x.

Answer 4

but i have to get 2 numbers.

Answer 5

A quadratic equation will yield two solutions.

Answer 6

i dont know how to do it

Answer 7

x^2 + y^2 = 100
y = x + 2
Take y from the second equation and substitute in the first equation:
x^2 + (x+2)^2 = 100
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 = 100
2 is a factor in each term. So divide throughout by 2:
x^2 + 2x + 2 = 50
x^2 + 2x - 48 = 0
x^2 + 8x - 6x - 48 = 0
x(x+8) - 6(x+8) = 0
(x-6)(x+8) = 0
x = 6 or -8

Answer 8

Thank you so much, can you help me with a different problem?

Answer 9

I can guide you but I do not wish to do the entire problem myself.

Answer 10

no, but it is hard for me because i have never done it before and im doing it online and they dont give examples but if you guide me that would be great

Answer 11

alright.

Answer 12

look, it is a graph

Answer 13

Take the top line first. What is its y-intercept?

Answer 14

it would be -4,2?

Answer 15

The y-intercept is -4. IDK where you are getting the 2 from.
Can you find the slope of the top line? slope = rise/run

Answer 16

becuase it is passing through the 2 but not exactly am i wrong?

Answer 17

That would be the x-intercept. It is passing between 2 and 3 and so it will be 2.5 or 5/2.
But the y-intercept is where the line cuts the y-axis and it is -4.
Getting back to the slope. What is the slope of the top line?

Answer 18

There may be an easier way to solve this without even finding the slope.
The y-intercept of the top line is -4
What is the y-intercept of the bottom line?

Answer 19

between -5 &-6 but i say -5?

Answer 20

Yes -5 is correct.
Remember, y intercept is where the line cuts the y-axis.
That means x = 0.
So put x = 0 and solve for y in each of the answer choices and see which one gives the y-intercepts for the two lines to be: -4 and -5 respectively.

Answer 21

so for example it would be ? an solve
a. 3(0) + 2y = 8
6(0) + 4y = 20

Answer 22

Yes. If the first part of the first choice does not give a -4 or a -5 move on to the next choice. You don't have to do the second part of the first choice.

Answer 23

okei thank you is there any way we can stay in contact?

Answer 24

What was your answer?

Answer 25

im working on it

Answer 26

I volunteer here when I have some time. No fixed schedule. But there are many individuals who can help. Right now the tagging, messaging, notifications, etc. have not been working properly for the past week or so. You can tag my name when you post a problem and if the notification works and I am logged in I can visit your page.

Answer 27

i got B

Answer 28

B) has 3x - 2y = 8 and 6x + 4y = 20. Put x = 0 in each and solve for y.
0 - 2y = 8. y = -4 4y = 20, y = 5
Gives -4 and 5 as y-intercepts. But we want -4 and -5. So it is not B.

Answer 29

D

Answer 30

Yes!

Answer 31

thank you

Answer 32

you are welcome.

Answer 33

have time for another one?

Answer 34

go ahead. one more.

Answer 35

Plot the three points given under the g(x) table.
IF any of the points falls on the parabola f(x) then it means g(x) and f(x) will intersect.
If no points of g(x) falls on the parabola it means they won't intersect.

Answer 36

and how do you do that eample';$

Answer 37

You are given 3 points belonging to g(x) in the table.
Treat the x value as the x-coordinate and the g(x) value as the y-coordinate.
The first point is (-1, 0). Plot that point on the graph and see if it lies on the parabola.
Try the other two points also.