To find the point where y = 2x - 1 and y = 7x + 8 meet we solve the two equations.

2x - 1 = 7x + 8

=> -5x = 9

=> x = -9/5

y = -18/5 - 1

=> -23/5

**The point of intersection is (-9/5, -23/5). This lies in the third quadrant.**

In the first quadrant the value of the x and y coordinates are positive, in the second quadrant the x-coordinate is positive but the y-coordinate is negative. In the third quadrant both the x and y coordinates have a negative value and in the fourth quadrant the x coordinate is negative while the y coordinate is positive.

To find where the lines y = 2x - 1 and y = 7x + 8 meet, first find the coordinates of their point of contact.

SubstituteĀ y = 2x - 1 in y = 7x + 8,

2x - 1 = 7x + 8

5x = -9

x = -9/5

y = 2x -1 = -18/5 - 1 = -23/5

As both the x and y coordinates of the point are negative, it lies in the third quadrant.