Problems

  1. For each ordered pair, determine whether it is a solution to the system of equations.

    $-3x+2y=5$

    $2x-5y=4$

     

    (a). $(1, 4)$

    (b). $(-3, -2)$

  2. Graph each of the following systems below and write its solution.

    (a)  $-2x+y=4$

       $y=-\dfrac{1}{2}x-1$

     

    (b)  $x-3y=-3$

       $y=\dfrac{1}{3}x+1$

     

    (c)  $-2x-2y=4$

       $y=-x-3$

  3. Use substitution to solve the systems.

    (a)  $x=3y+16$

      $-3x+5y=-28$

     

    (b)  $3x-5y=-23$

      $-2x+y=6$

  4. Solve the following systems of equations (use the elimination method)

    (a).  $x+4y=17$

      $-x-6y=-23$

     

    (b).  $5x-4y=6$

      $3x-2y=4$

     

    (c).  $2x+3y=3$

      $-3x-7y=-12$

Answer key

  1. (a). No

    (b). Yes

  2. (a) graph

    Solution: $(-2, 0)$

    (b) graph

    Infinitely many solutions.

    (c) graph

    No solution.

  3. (a). $x=1$ and $y=-5$

    (b). $x=-1$ and $y=4$.

  4. (a). $x=5$ and $y=3$

    (b). $x=2$ and $y=1$

    (c). $x=-3$ and $y=3$