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

1.	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» 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.

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»

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.