math
posted by Anirudh Mahapatro .
How many pairs of integers (x,y) satisfy the conditions y=3x1,6x2y=2 and 0<=x<=25?

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