### Home > CCA2 > Chapter 10 > Lesson 10.2.1 > Problem10-101

10-101.

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

1. $2x + y = 12$
$xy = 16$

1. $2x + y = 12$
$xy = 20$

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

Note that other sequences of steps are possible.

$y = 12 - 2x$

$x(12 - 2x) = 16$

$12x − 2x^2 - 16 = 0$

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

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

$x = 4$ or $x = 2$

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.