Question

x + y = 5 and 2x + 2y= 10 are two equations in two variables. 

Find live different solutions of x + y = 5, verify whether same solutions satisfy the equation 2x + 2y = 10 also. Observe both equations.

Find the condition where two equations in two variables have all solutions in common.

Answer 1

Five solutions of x + y = 5 are given below:

 (1,4), (2, 3), (3, 2), (4,1), (0, 5) 

The above solutions also satisfy the equation 2x + 2y = 10. 

∴ x + y = 5 …[Dividing both sides by 2] 

∴ If the two equations are the same, then the two 

equations in two variables have all solutions common.