Question

The sum of two angels are x and y . If 3x + y = 1 and 4/x + 5y = 2 .Find x,y

Answer 1

According to Question, 

3x + y = 1       Eqn 1
4/x + 5y = 2      
4 + 5xy = 2x     Eqn 2

From Eqn 1

y = 1- 3x

Put y in Eqn 2 we get

4 + 5x ( 1-3x) = 2x
4 + 5x - 15 x^2 = 2x
15x^2 - 3x - 4 = 0
3x ( 5x - 1 ) = 4

Thus,

x = 1
So  
y = 1 - 3x
   = -2

Answer 2

These are simultaneous Equations and thus we solve them simultaneously.

SOLUTION:

3x + y = 1........(i)
4/x + 5y =2..........(ii)

From equation (i) : y= 1 - 3x

We substitute this in equation (ii) :

4/x + 5(1 - 3x) = 2

4/x - 15x + 5 = 2

4/x - 15x = - 3

15x² - 3x - 4=0 (quadratic equation)

Solving for x using the quadratic formula :

x ={ 3 +/-√(9+240)} /30

x=18.779/30 =0.63 or - 12.77/30= - 0.43

Taking the positive value of x we have: x= 0.63

Substituting in equation (i) we get :

3 × 0.63 + y = 1

1.89 + y =1

y = - 0.89

Find attached the quadratic formula.