Chapter 4, Problem 1RE

For Exercises 1–4, determine if the ordered pair is a solution to the system.

$\begin{array}{c}x-4y=-4\left(4,2\right)\\ x+2y=8\end{array}$

To determine

Whether the ordered pair $\left(4,2\right)$ is the solution of the system of lines:

$\begin{array}{ccc}\hfill x-4y& =& -4\hfill \\ \hfill x+2y& =& 8\hfill \end{array}$

Answer to Problem 1RE

Solution:

The given ordered pair is the solution of the given system of lines.

Explanation of Solution

Given Information:

The system of lines:

$\begin{array}{l}x-4y=-4\\ x+2y=8\end{array}$

A set of ordered pair is a solution for a given set of lines if it satisfies the equation of lines.

For $x-4y=-4$,

Substitute $x=4$ and $y=2$ in the above equation as follows:

$\begin{array}{l}4-\left(4\times 2\right)\stackrel{?}{=}-4\\ 4-8\stackrel{?}{=}-4\\ -4=-4\end{array}$

Which is true.

So, the point $\left(4,2\right)$ satisfies the given equation.

For $x+2y=8$,

$\begin{array}{l}4+\left(2\times 2\right)\stackrel{?}{=}8\\ 8=8\end{array}$

Which is true.

So, the point $\left(4,2\right)$ satisfies the given equation.

Here, $\left(4,2\right)$ satisfies both the equations.

Therefore, the given ordered pair is the solution of the given system of lines.