Consider the linear system Where t is a nonzero constant. a. Determine the x-...

Consider the linear system

Where t is a nonzero constant.

a. Determine the x- and y-intercepts of the lines x+y = 1 and x+(t/2)y = t; sketch these lines. For which values of the constant t do these lines intersect? For these values of t, the point of intersection (x, y) depends on the choice of the constant t; that is, we can consider x and y as functions of t. Draw rough sketches of these functions.

Explain briefly how you found these graphs. Argue geometrically, without solving the system algebraically.

b. Now solve the system algebraically. Verify that the graphs you sketched in part (a) are compatible with your algebraic solution.