Solve each system below.

1. $\left. \begin{array}[t] { l } { 2 x + y = 12 } \\ { x y = 16 } \end{array} \right.$ 

   Step 1(a):

   Note that other sequences of steps are possible.

   Step 2(a):

   Step 3(a):

   Step 4(a):

   Step 5(a):

   Step 6(a):

   Step 7(a):

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

   Now try part (b) on your own.

   $y = 12 − 2x$

   $x\left(12 − 2x\right) = 16$

   $12x − 2x^{2} − 16 = 0$

   $x^{2} − 6x + 8 = 0$

   $\left(x − 4\right)\left(x − 2\right) = 0$

   $x = 4$ or $x = 2$

2. $\left. \begin{array}[t] { l } { 2 x + y = 12 } \\ { x y = 20 } \end{array} \right.$ 

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

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