How do I solve this

Question

4x + 5y =100 

5x + 4y =62

If the system of equations above has solution (x,y) what is the value of x+y ? 

 

A. 0 

 

B. 9 

 

C. 18 

 

D. 38 

Answer 1

Multiply the first equation by 5 and the second equation by -4:

 

    20x + 25y = 500

   -20x - 16y = -248

 

Add the equations to obtain 9y = 252

 

So, y = 252/9 = 28

 

4x + 5(28) = 100

 

4x + 140 = 100

 

          4x = -40

 

            x = -10