After combining the $x$-terms, multiply the entire equation by the least common multiple of $10$, $7$, and $35$.

For no solution, the $x$- and $y$-coefficients must be in the same ratio between the two equations, but the constants must not be in that ratio.

Enter 4/5 x - 6/7 y = 8/35 + 1/10 x in Desmos.

Enter each option as a second equation (one at a time).

Choose the option whose graph is a different line that never intersects the first line (parallel lines with different intercepts).

Start with

Move the $x$-term on the right to the left:

Compute the coefficient:

so

Multiply both sides by $70$:

Two linear equations have no solution when they are parallel but not the same line.

In standard form, that means the $x$- and $y$-coefficients are proportional, but the constant term is not proportional by the same factor.

We want an answer choice where the left side is $k(49x-60y)$ for some constant $k$, but the right side is not $k\cdot 16$.

For $-98x+120y=-35$, the left side is

If it were the same line as $49x-60y=16$, the constant would be $-2\cdot 16=-32$, but the choice has $-35$.

So the lines are parallel and distinct, giving no solution. Therefore, the second equation could be $-98x+120y=-35$.