TWO linear equations with different slopes intersect in one point, regardless
of their y-intercepts. That point is the solution of the pair.
However, this does not mean that three (or more) equations in two variables, even if they meet the above conditions, have a solution.
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The slopes (gradients) of the two equations are different.
One solution
The graph of a system of equations with the same slope will have no solution, unless they have the same y intercept, which would give them infinitely many solutions. Different slopes means that there is one solution.
Two linear equations (or lines) with the same y-intercept and different slopes are intersecting lines. They intersect at the y-intercept. If the slopes are negative reciprocals (ex: one slope is 3 and one slope it -1/3) then they are perpendicular lines.
no solution