Question

How do you work this non linear simultaneous equation (with working out)

x^2 + y^2 = 29
x - y = 7

Please with working out ^^^^^ And how to do it :]

Answer 1

to get a geometric idea of what you're looking at . . . the first equation is a circle, and the second equation is a line.

that means there are three possible scenarios:

a.) the line never intersects the circle (no solution)
b.) the line is tangent to the circle (one solution)
c.) the line intersects the circle twice (two solutions)

try setting the second equation equal to x:

x = y + 7

and then

substituting this value of x into the first equation

Answer 2

How ? :S

Answer 3

like this:

(y +7)^2 + y^2 = 29

Answer 4

Right, then what do you do to it after that ?

Answer 5

solve for y. try expanding (y + 7)^2

Answer 6

Thats the whole problem, I don't know how to do it!

Answer 7

review how to FOIL because that's all it is:

(y +7)(y +7)

Answer 8

I give up, I don't understand what FOIL is and how to do the question. Ill find somewhere else...

Answer 9

http://en.wikipedia.org/wiki/FOIL_method

its just a basic algebra method of multiplying two things

(y +7)(y +7) =

First: y*y
Outer: y*7
Inner: y*7
Last: 7*7

Add them up

y^2 + 14y + 49

Answer 10

Then what do you do after that ?

Answer 11

your question is:

here is a circle, and here is a line. do they intersect? if so, where do they intersect?

you are given the equation of the circle, and the equation of the line.

so all we need to do is find out whether or not they have any points (coordinates) in common.

one way to determine that is by what we are doing right now. if the circle and the line do have a common point, then the x-value of that point will be the same in both equations.

so we solve for x in one equation, and then substitute that value into the other equation.

the equation of the line, when solved for x, was:

x = y + 7

then we used this value of x and substituted it into the other equation

(y +7)^2 + y^2 = 29

now we are down to one equation with one variable

to solve for y you have to expand the left side by FOILing as mentioned earlier. you end up with:

y^2 + 14y + 49 + y^2 = 29

then combine like terms

2y^2 + 14y + 49 = 29

subtract 29 from both sides to get the equation = 0

2y^2 + 14y + 20 = 0

from here just divide everything by 2

y^2 + 7y + 10 = 0

use knowledge of factoring to factor this into

(y + 2)(y +5) = 0

your two values of 'y' are:

y = -2
y = -5

this means there are two corresponding 'x' values. to figure out what they are, refer back to the original second equation:

x - y =7

let y = -2, solve for x

x - (-2) = 7
x + 2 = 7
x = 5

so when x = 5, y = -2. that means (5, -2) is one solution

the other solution is found when you let y = -5

x - (-5) =7
x + 5 =7
x = 2

so when x = 2, y = -5, that means (2, -5) is another solution

and so the two solutions are:

(5, -2) and (2, -5)

Answer 12

Thanks a lot!!!!!!!! :D

Answer 13

np