SOLUTION: is it the right way to square root the whole equation for example: x^2 + y^2 = 16 because i have to find the point of interse2ction of that equation and 2y + x = 3 what i did w

Algebra ->  Radicals -> SOLUTION: is it the right way to square root the whole equation for example: x^2 + y^2 = 16 because i have to find the point of interse2ction of that equation and 2y + x = 3 what i did w      Log On


   

Question 702419: is it the right way to square root the whole equation
for example: x^2 + y^2 = 16
because i have to find the point of interse2ction of that equation and 2y + x = 3
what i did was i put square root on the first equation and then solve it by simultaneous equation however i have got the wrong answer.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
is it the right way to square root the whole equation
for example: x^2 + y^2 = 16
find the point of interse2ction of that equation and 2y + x = 3
-----------------
2y + x = 3
x = -2y + 3
Sub for x in the other eqn
(-2y + 3)^2 + y^2 = 16
4y^2 - 12y + 9 + y^2 = 16
5y^2 - 12y - 7 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-12x%2B-7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-12%29%5E2-4%2A5%2A-7=284.

Discriminant d=284 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+284+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+284+%29%29%2F2%5C5+=+2.88522995463527
x%5B2%5D+=+%28-%28-12%29-sqrt%28+284+%29%29%2F2%5C5+=+-0.485229954635272

Quadratic expression 5x%5E2%2B-12x%2B-7 can be factored:
5x%5E2%2B-12x%2B-7+=+%28x-2.88522995463527%29%2A%28x--0.485229954635272%29
Again, the answer is: 2.88522995463527, -0.485229954635272. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-12%2Ax%2B-7+%29

-----------
y = 6/5 + sqrt(71)/5
x = -2y + 3
x = -12/5 - 2sqrt(71)/5 + 3
--> point (3/5 - 2sqrt(71)/5,6/5 + sqrt(71)/5)
========================
y = 6/5 - sqrt(71)/5
x = -2y + 3
x = -12/5 + 2sqrt(71)/5 + 3
--> point (3/5 + 2sqrt(71)/5,6/5 - 2sqrt(71)/5)