How many pairs of integers (x,y) satisfy the conditions y=3x-1,6x-2y=2 and 0<=x<=25?

Answer 1

6 x - 2 y = 2 Subtract 6 x to both sides

6 x - 2 y - 6 x = 2 - 6 x

- 2 y = 2 - 6 x Divide both sides by - 2

- 2 y / - 2 = 2 / - 2 - 6 x / - 2

y = - 1 + 3 x

y = 3 x - 1

Equations :

y = 3 x - 1 and 6 x - 2 y = 2 are same equation.

On interval 0 < = x < = 25 you have 26 integers :

0 = first integer

1 = second integer

2 = third integer

...

25 = twenty-sixth integer

You have 26 pairs of integers ( x , y ) which satisfied given conditions.