Solve the following system.
x 2 + y 2 = 25
2x + y = 10
The solution set {(________,__________,_________,________)}

- anonymous

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- anonymous

i need 4 answers!!!

- anonymous

but how would you do that i only got 2

- welshfella

use the substitution method
from the second equation
y = 10 - 2x
Now replace y in the first equation by 10-2x to get an equation in x only
solve this for x ( there will be 2 values of x)

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## More answers

- anonymous

this is what i got
2x+y=10;2x+2y=25
Step: Solve 2x+y=10 for y:
2x+y+−2x=10+−2x(Add -2x to both sides)
y=−2x+10
Step: Substitute (−2x+10) for y in 2x+2y=25:
2x+2y=25
2x+2(−2x+10)=25
−2x+20=25(Simplify both sides of the equation)
−2x+20+−20=25+−20(Add -20 to both sides)
−2x=5
−2x−2=5−2(Divide both sides by -2)
x=−52
Step: Substitute (−52) for x in y=−2x+10:
y=−2x+10
y=−2(−52)+10
y=15(Simplify both sides of the equation)
Answer:
y=15 and x=−52

- welshfella

you can then find the corresponding values of y by substituting back in equation 2

- anonymous

mm

- anonymous

so can you solve this for me please and then explain after

- anonymous

Im confused

- welshfella

do you follow my method?

- anonymous

Not really but please can you do it and explain?

- welshfella

2x + y = 10
subtract 2x from both sides
y = 10 - 2x
OK with that?

- anonymous

yes i am

- welshfella

right
x^2 + y^2 = 25
replace the y in the above equation by 10 - 2x:-
x^2 + (10- 2x)^2 = 25
x^2 + (10 - 2x)(10 - 2x) = 25
expanding the brackets:-
x^2 + 100 -20x-20x + 4x^2 = 25
adding like terms
5x^2 - 40x + 100 = 25
5x^2 - 40x + 75 = 0

- anonymous

alright

- welshfella

so now we need to solve this quadratic
you can make it easier by dividing each term by 5:-
giving
x^2 -8x + 15 = 0

- welshfella

can you solve this?
you need to factor first
you need 2 numbers whose product is 15 and when added = -8

- anonymous

just do it foe me sir i have limited time

- welshfella

(x - 3)(x - 5) = 0
x = 3 or 5
now plug x=3 into the second equation 2x + y = 10 and find y
then do the same for x = 5 and you have your 4 solutions

- anonymous

i dont have a calculator

- welshfella

you dont need one to these

- anonymous

i got 4,8,10 and 12 is that correct

- welshfella

2(3) + y = 10
6 + y = 10
y = ?

- anonymous

if not what are they

- welshfella

if already got 2 values of x :- 3 and 5
now we need values of y

- welshfella

6 + y = 10
y = ?
i'm sure you can do that

- anonymous

its 4

- welshfella

right
now plug in x = 5 to find the second value of y

- anonymous

0?

- welshfella

yes

- welshfella

he has the answers now

- anonymous

so its 3,5,4,0?

- anonymous

lol my fault

- welshfella

yes
but pair them up ( x,y)
(5,0) and (3,4)

- anonymous

but i have 4 answer boxes?

- welshfella

well enter then as 5 0 3 4

- anonymous

look at the flick of the wrist

- anonymous

thanks

- anonymous

np

- welshfella

yw

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