Question

solve the system of equations 4x-8y=0, x^2 +y^2=25

Answer 1

The system of equations are

4x - 8y  =  0 --------------> (1)

x^2 + y^2  =  25 -----------------> (2)

From Eq (1)

4x  =  8y

x  =  (8y) / 4

x  =  2y ----------> (3)

Substitute x = 2y in Eq (2)

(2y)^2 + y^2  =  25

4y^2 + y^2  =  25

5y^2  =  25

y^2  =  25/5

y^2  =  5

Apply Square root on each side

y  =  ±√5

y  = √5  and y  =  -√5

Substitute y  = √5 in Eq (3)

x  =  2√5

Substitute y  = -√5 in Eq (3)

x  =  2(-√5)

x  =  - 2√5

Answer :

The solutions are y = √5, x  =  2√5 and y = -√5, x  =  - 2√5.