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Do Number 6 first so you can do the rest

6. Consider the system of equations ax + by = k cx +dy1 ex + fy- m Discuss the relative positions of the lines ax + by k, cx + dy l, and ex +fy m when: (a) the system has no solutions (b) the system has exactly one solution (c) the system has infinitely many solutions

7. Show that if the system of equations in Exercise 6 is consistent, then at least one equation can be discarded from the system without altering the solution set. 8. Let k I m 0 in Exercise 6; show that the sy 0 in Exercise 6; show that the system must be consistent. What can bo e system has exactly one solution? said about the point of intersection of the three lines if th 9. Consider the system of equations Show that in order for this system to be consistent, a, b, and c must satisfy c a+ b. 10. Prove: If the linear equations X1 +kx2 = c and xi + lx,-d have the same solution set then the equations are identical.

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