Question

Is y=-13/6x+5/3 same as 13x+6y=10 ?

Answer 1

Yes:
13x + 6y = 10
-13x        -13x
_______________
         6y = -13x + 10
        
Divide 6y, 13x, and 10 by 6

y = -13/6x + 10/6

Simply 10/6 by finding the least common multiple of the numerator and denominator, which is 2. 10 divided by 2 is 5, and 6 divided by 2 is 3. 10/6 = 5/3

Solution:
y = -13/6x + 5/3