If we multiply these three equations by 6, 2, and - 2 we have identically
6(2x - 3y + 5) + 2(3x - 4y - 7) - 2(9x - 5y - 8) = 0.
The coordinates of the point of intersection of the first two lines make the first two brackets of this equation vanish and hence make the third vanish. The common point of intersection of the first two therefore satisfies the third equation. The three straight lines therefore meet in a point.
