Solve for $x$ and $y$ in each system below. .

3. Explain how the graphs of (a) and (b) relate to the solutions to each system of equations.

   Step 1(a):

   Note that other sequences of steps are possible.

   $y = 12 - 2x$

   Step 2(a):

   $x(12 - 2x) = 16$

   Step 3(a):

   $12x − 2x^2 - 16 = 0$

   Step 4(a):

   $x^2 - 6x + 8 = 0$

   Step 5(a):

   $(x - 4)(x - 2) = 0$

   Step 6(a):

   $x = 4$ or $x = 2$

   Step 7(a):

   When $x = 4$, $y = 4$, so $(4, 4)$ is a solution.
   When $x = 2$, $y = 8$, so $(2, 8)$ is a solution.

   Now try part (b) on your own.