### Home > INT3 > Chapter 10 > Lesson 10.3.2 > Problem10-174

10-174.

Solve each system below.

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

Note that other sequences of steps are possible.

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. $\left. \begin{array} { l l \quad } & { 2 x + y = 12 } \\ { } & { x y = 20 } \end{array} \right.$

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