1. Under what condition on $y_1$ , $y_2$ , $y_3$ do the points $(0, y_1 )$, $(1, y_2 )$, $(2, y_3 )$ lie on a straight line?
  2. Use elimination to solve
\[\begin{cases} u + v + w = 6\\\\ u + 2v + 2w = 11\\\\ 2u + 3v − 4w = 3 \end{cases}\]

and

\[\begin{cases} u + v + w = 7\\\\ u + 2v + 2w = 10\\\\ 2u + 3v − 4w = 3\\\\ \end{cases}\]
  1. Prove the following statements:

    1. Prove that if the determinant of the coefficient matrix for the following system of linear equations

      \[\begin{cases} ax+by=k\\\\ cx+dy=l \end{cases}\]

      is non-zero, then this system has a solution.

    2. Prove that if a system of two linear equations with two unknowns has more than one solution, it must have infinitely many solutions.