Ok I'm still confused please help?

Question

ok before I didn't do FOIL, so now I've done it but I'm still stuck:
x^2 + y^2 = 10
x + 2y = 7

x^2 + y^2 = 10
2y = 7-x
y = 7/2 - x/2
x^2 + (7/2 - x/2)^2 = 10
x^2 + 49/4 - 7x/4 - 7x/4 - x^2/4 = 10
x^2 + 49/4 - 14x/4 - x^2/4 = 10
4x^2 + 49 -14x -x^2 = 40
3x^2 -14x+49 = 40

......so where do I go from here to find x....or have I done something wrong again?

oooh I see what I did!!
thanks!

Answer 1

You've got the right method and you are very close, but I see a problem when you mulplied -x/2 * -x/2... you should get +x²/4 (positive).

If you do that, you'll get to:
5x² - 14x - 9 = 0

This can easily be factored to:
(5x - 9)(x - 1) = 0

Your solutions are:
x = 1, y = 3
or
x = 9/5, y = 13/5

So the line crosses the circle at:
(1, 3) and (1.8, 2.6)

A double check confirms:
x² + y² = 10

Case 1:
1² + 3² = 10 check

Case 2:
(9/5)² + (13/5)² =? 10
81/25 + 169/25 =? 10
250/25 =? 10
10 = 10 check

Similarly:
x + 2y = 7
1 + 2(3) =? 7
1 + 6 = 7 check

9/5 + 2(13/5) =? 7
9/5 + 26/5 =? 7
35/5 = 7 check

The intersection points of the line and circle are:
(1, 3) and (9/5 , 13/5)

Answer 2

x^2 + y^2 = 10
x + 2y = 7

x^2 + y^2 = 10
2y = 7-x
y = 7/2 - x/2
x^2 + (7/2 - x/2)^2 = 10
x^2 + 49/4 - 7x/2 + x^2/4 = 10
x^2 + 49/4 - 7x/2 + x^2/4 = 10
4x^2 + 49 -14x +x^2 = 40
5x^2 -14x+9 = 0
(5x+14)(x-1)=0
then x = 14/5 or x = 1
and get the value of y by substituting in any of the two functions

Answer 3

x^2 + y^2 = 10
2y = 7-x
y = 7/2 - x/2
x^2 + (7/2 - x/2)^2 = 10
x^2 + 49/4 - 7x/4 - 7x/4 - x^2/4 = 10 <-- should be +x^2/4
x^2 + 49/4 - 14x/4 + x^2/4 = 10
4x^2 + 49 -14x +x^2 = 40
5x^2 -14x+49 = 40
5x^2 -14x +9 =0
(5x - 9)(x- 1) =0
5x-9 = 0 --> x = 1.8
x-1 = 0 --> x = 1

Answer 4

first, devide the term by 3, so taht you have x² without that 3 in front and pull the 40 to the left..
: x² -14x/3 + 49/3 -40/3= 0
x1= 7/3 + radical of 22/9
x2= 7/3 - radical of 22/9

the answer is : x1= about 3.9
x2= about 0.77
these answers are just slightly derived from the originals, since I didn't watned to copy 20digits after the . <-- point
I tried to write you the formula with which i solved it, but it will rather complicate things, so I'll let it out.

Answer 5

You have a sign error:
x^2 + 49/4 -7x/4 -7x/4 + x^2/4 = 10 <--- last term on left side is +

Then you are okay, just use quadratic equation.

Answer 6

Write the equation as 3x^2 - 14x + 9 = 0, and use the quadratic formula.

Answer 7

OK you put a - in front of x²/4 there should be a +.
That would get you 5x² and 9 when you bring the 40 over
will give you a factorable polynomial