Solve the equation...

Question

X^2 + y^2 = 10

X^2 - 5xy + 6y^2

Please solve this equation and what is the class of this equation?

Answer 1

This is a simultaneous linear and non-linear equation.

Solution:

2x+2y=10-----(1)

2x-5xy+12y=0---(2)

Simplify (1)

x+y=5----(1)

x=5-y

Substitute (x) into (2):

=> 2(5-y)-5y(5-y)+12y=0

=> 10-2y-25y+5y²+12y=0

=> 5y²-15y+10=0

Divide the equation by 5 to simplify:

=y²-3y+2=0

(Solve the equation via calculator/middle term breaking)

y= 1 or 2

y(1) in eq. (1):

x+1=5

x= 4

y(2) in eq. (2):

x+2=5

x=3

Therefore, (x,y)= (4,1),(3,2). [Ans]