Question 698848: Solving Non-Linear Systems?
x^2+y^2=35
4x^2-9y^2=36
Please show step by step. Thank You.
---Jawairia N. Found 2 solutions by Simnepi, Alan3354:Answer by Simnepi(216) (Show Source):
You can put this solution on YOUR website! To solve equations of this type just think of the squared terms as being linear terms(if that makes sense!)
x^2 + y^2 = 35 Equation (1)
4x^2 - 9y^2 = 36 Equation (2)
Rearranging (1) gives
x^2 = 35 - y^2 Equation (3)
Substitute this value into (2) giving
4(35 - y^2) - 9y^2 = 36
Therefore
140 - 4y^2 -9y^2 = 36
Simplifying and gathering terms to either side gives
-13y^2 = -104
therefore
y^2 = 8
Substitute this value into (1) giving
x^2 + 8 = 35
Therefore
x^2 = 27
now the values of x and y are
y = and x =
You can put this solution on YOUR website! Solving Non-Linear Systems?
x^2+y^2=35
4x^2-9y^2=36
===============
The other tutor got the right values, but there are 4 combinations, 4 intersections.
Use plus and minus for the x & y values.
