finding unknown vertices of triangle from line equations

[Motherof8]

The problem states: Lines y = 3 + 2/3x, y =-1/3x, and y = -4/3x +3 intersect to form a triangle. Find the verticies. I solved for x by substituting x for y, then I solved for y and started to plot the lines on a graph. I get a constant value for x, and different values for y, which doesn't form a triangle. Did I do the wrong thing?

[maggiemagnet]

The problem states: Lines y = 3 + 2/3x, y =-1/3x, and y = -4/3x +3 intersect to form a triangle. Find the verticies. I solved for x by substituting x for y, then I solved for y and started to plot the lines on a graph. I get a constant value for x, and different values for y, which doesn't form a triangle. Did I do the wrong thing?

Without seeing what you got or how, it's hard to say. But you might want to start with the fact that the corners of the triangle are where pairs of lines cross. So pick a pair of lines and find the intersection for that pair. That's one corner. Then do a different pair. Then do the last pair. You should get three points. Each one is the "solution" to a "system" that you made up by pairing lines, and each is also a corner point of the triangle.