Solve the system by addition

Question

5x – 3y = 13 and 4x – 3y = 11?

Answer 1

5x – 3y = 13   -----(1)

4x – 3y = 11   -----(2)

Multiply the eqation (1)  with  4  and

Multiply the eqation (2)  with   -5

  4×(5x – 3y = 13) =    20x -12y =   52

 -5×(4x – 3y = 11)  =  -20x +15y = -55

Now add the resultant two eqations.Inorder to add 2 eqations, group like terms and combine them.

20x + (-20x) -12y +15y = 52 +(-55)

⇒  3y = - 3       

⇒  y = -1

Now substitute y= -1 in eqation (1)

     5x -3(-1) =13

⇒  5x + 3 = 13

⇒  5x +3 -3 = 13 -3

⇒  5x = 10

⇒  x = 2

The values of x and y are  2 , -1  respectively