construct a system of equations ive to construct a system of

construct a system of equations

i\'ve to construct a system of equations

ax^2+by^2=c

dx^2+ey^2=f

the system has 2 solutions

Solution

I\'ll give you the following practical example.

We\'ll change the first equation in:

y^2 = 25 - x^2

We\'ll substitute y^2 in the second equation:

16x^2 + 25(25 - x^2) = 400

We\'ll remove the brackets:

16x^2 + 625 - 25x^2 - 400 = 0

We\'ll combine like terms:

-9x^2 = -225

We\'ll divide by -9:

x^2 = 25

x1 = 5

x2 = -5

We\'ll substitute x1 and x2 in the first equation:

y1^2 = 25 - 25

y1^2 = 0

y1 = y2 = 0

The solutions of the system are {5 ; 0} and {-5 ; 0}.