SOLUTION: 1. 3x -2y =0 x^2+(y-1)^2=11 2. 6x +12y^2-18=0 y+3x-9=0 3.12x^2-y^2-12=0 y-2 =0 4. 8x^2-y^2+16y-18=0 2y^2-48x -16y - 3 = 0 Good day Sir/Mam! What is t

Algebra ->  Systems-of-equations -> SOLUTION: 1. 3x -2y =0 x^2+(y-1)^2=11 2. 6x +12y^2-18=0 y+3x-9=0 3.12x^2-y^2-12=0 y-2 =0 4. 8x^2-y^2+16y-18=0 2y^2-48x -16y - 3 = 0 Good day Sir/Mam! What is t      Log On


   

Question 1093133: 1. 3x -2y =0
x^2+(y-1)^2=11
2. 6x +12y^2-18=0
y+3x-9=0
3.12x^2-y^2-12=0
y-2 =0

4. 8x^2-y^2+16y-18=0
2y^2-48x -16y - 3 = 0
Good day Sir/Mam!
What is the solution set of this non linear equation and the steps?
Thank You I truly appreciate your website.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. 3x -2y =0
x^2+(y-1)^2=11
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3x -2y =0
3x = 2y
9x^2 = 4y^2
----
x^2+(y-1)^2=11
9x^2 + 9(y-1)^2 = 99
Sub for 9x^2
4y^2 + 9y^2 - 18y + 9 = 99
13y^2 - 18y - 90 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 13x%5E2%2B-18x%2B-90+=+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=%28-18%29%5E2-4%2A13%2A-90=5004.

Discriminant d=5004 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+5004+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+5004+%29%29%2F2%5C13+=+3.41303679751191
x%5B2%5D+=+%28-%28-18%29-sqrt%28+5004+%29%29%2F2%5C13+=+-2.02842141289652

Quadratic expression 13x%5E2%2B-18x%2B-90 can be factored:
13x%5E2%2B-18x%2B-90+=+%28x-3.41303679751191%29%2A%28x--2.02842141289652%29
Again, the answer is: 3.41303679751191, -2.02842141289652. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-18%2Ax%2B-90+%29

y = the unfortunate answers shown.
-----
x = 2y/3
===========================

2. 6x +12y^2-18=0 --> 3x + 6y^2 - 9 = 0
---
y+3x-9=0
3x = -y+9
Sub for 3x in the 1st eqn.
===============
3.12x^2-y^2-12=0
y-2 =0
y = 2
Sub for y
====================
4. 8x^2-y^2+16y-18=0
2y^2-48x -16y - 3 = 0
Solve eqn 2 for x, then sub for x in eqn 1.
=================
Check for extraneous solutions.