## anonymous one year ago system of equation y=x^2+3 y=x+5

1. anonymous

if anyone could show me the steps?

2. anonymous

We generally use one to solve the other. Start with simplest. y = x + 5 y(-5) = x+ 5 (-5) y- 5 = x therefore substituting in eq .1 we get: y = (y-5)^2 +3 y = (y^2 -10y +25) + 3 y = y^2 -10y + 22 subtract y from both sides to get: 0 = y^2 -9y + 22 solve to get: |dw:1439459437832:dw|

3. anonymous

|dw:1439459686316:dw|

4. anonymous

so @BPDlkeme234 so the answer is 9 +or- 72over 22

5. myininaya

y = (y-5)^2 +3 y = (y^2 -10y +25) + 3 this should actually come to y^2-10y-y+25+3=0 y^2-11y+28=0 can you finish solving for y y^2-11y+28 is factorable

6. anonymous

@myininaya how would I factor y^2

7. myininaya

why would you want to factor y^2?

8. myininaya

y^2 is already in factored form... I was wanting you to factor y^2-11y+28

9. myininaya

what two numbers multiply to be 28 and add up to be -11?

10. anonymous

y7 and y4 @myininaya

11. myininaya

-7(-4)=28 -7-4=-11 so y^2-11y+28=(y-7)(y-4)

12. myininaya

so you can solve (y-7)(y-4)=0 by solving both y-7=0 or y-4=0

13. myininaya

once you find the y's then plug each y into: $x=y-5$

14. anonymous

I still do not understand why im sorry im vary lost @myininaya

15. myininaya

understand what exactly?

16. myininaya

factoring?

17. myininaya

if you don't understand how to factor you can use the quadratic formula since it is a quadratic equation

18. myininaya

$ax^2+bx+c=0 \\ \implies x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

19. myininaya

$y^2-11y+28=0 \\ \implies y=\frac{-(-11) \pm \sqrt{(-11)^2-4(1)(28)}}{2(1)}$ do you understand how to simplify this?

20. anonymous

I don't know how to find the answer I thought he answer was y7 and x4

21. myininaya

before we can find the ordered pairs we have to find the y values do you know how to solve the equation y^2-11y+28=0?

22. myininaya

when you say things like y7 does that mean y=7?

23. myininaya

if so when you said "y7 and y4 " which actually in your case means y=7 or y=4 then that is right for the y's... now you had x=y-5 now if y=7 then x=7-5=? and if y=4 then x=4-5=? so the ordered pairs are (7-5,7) (4-5,4)

24. myininaya

just need to simplify the x-coordinates for each point