Using the XY Coordinate system

Question

Draw a line through the point (4, 0) and (7, -2) and another line through the
points (-1, -4) and (7, -2) on the same coordinate system. Do the lines
intersect? If there is an intersection what does it mean? Would you consider any
points of intersection a solution of both linear equations on the graph?
Explain.

Answer 1

Both lines pass through (7, -2), therefore that is the intersection point.

The linear equations that define these two lines are:

y = -2/3 x + 8/3

y = 1/4 x -15/4

In both cases, substituting 7 for x will yield -2 for y.  (7, -2) is the solution for this system of equations.