## raebaby420 2 years ago Please Help c: What are the solutions to the following system of equations? y = x2 + 12x + 30 8x − y = 10 (−4, −2) and (2, 5) (−2, −4) and (2, 5) (−2, −4) and (5, 2) No Real Solutions

1. raebaby420

What is the solution to the following system of equations? y = x2 + 10x + 11 y = x2 + x − 7 (−2, −5) (2, −5) (−2, 5)

2. campbell_st

rewrite the 2nd equation with y as the subject y = 8x - 10 now equate it to the 1st equation and you get \[8x - 10 = x^2 + 12x + 10\] now you have 1 equation in 1 unknown to solve

3. myko

y = x2 + 12x + 30 8x − y = 10 express y from second equation: \(y=8x-10\) substitute in the 1º equation: \(8x-10=x^2 + 12x + 30\) rearange terms: \(x^2+4x+40=0\) solve this. You will get 2 solutions, which later substitute in the 2º equation to get corresponding y value

4. campbell_st

oops should be ' \[8x - 10 = x^2 + 12x + 30\] just solve for x

5. raebaby420

Mm.. ill try. One sec, ill let you know what I get

6. missMob

:O maths

7. campbell_st

and can you check your equations as they may be a typo in them...

8. nirmalnema

you can get the ans by by making the quadratic eq..in x

9. missMob

we will put all the x on one side

10. raebaby420

The what? LOL

11. campbell_st

because based on the information there are any solutions that are real numbers

12. campbell_st

oops... which is an option

13. campbell_st

sorry...

14. raebaby420

Ok.. so its D.. cool

15. missMob

maths is confusing

16. raebaby420

But idk how to get D

17. missMob

*takes out the gun shoots maths*

18. campbell_st

well do you know about the discriminant...? thats how you check...

19. raebaby420

lol...

20. raebaby420

No.. but I got 8x-10=x2+12x+30 so far..

21. raebaby420

What do I do from there?

22. campbell_st

subtract 8x from both sides... then add 10 to both sides of the equation...

23. raebaby420

Oh.. I knew that. For some reason I thought I needed to bring my X from the right to the left.

24. raebaby420

Ok.. so I got x=x2+4x+40 Is that right?

25. nirmalnema

ya you got it right

26. campbell_st

and the discriminant is for a quadratic \[ax^2 + bx + c = 0\] thew discriminant is \[b^2 - 4ac\] you have a = 1, b = 4 and c = 40 it will be less than zero... meaning complex roots

27. raebaby420

Sooo its D.

28. raebaby420

Thanks everyone! c:

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