# How to determine the number of solutions in a linear system without solving: 2x - 3y = 4 and 6y = 4x + 15?

##### 1 Answer

No solution

#### Explanation:

First, let's move either

If we check the ratio between the coefficients of

What remains to be checked is whether the lines are coincidental or not. If the lines are coincidental, there are infinitely many solutions. Otherwise, there is no solution. If we check out the constant for both equations, we can see that they are not the same

We can now conclude that the lines are not coincidental.

Hence, there is no solution.

Yes, we did a little bit of "solving". But once you get used to it, you'll be able to know without solving.