Chapter 13, Problem 1VR

Complete each statement with the correct term from the column on the right. Some of the choices may be used more than once and some may not be used at all. algebraic graphical intersection union infinitely many solutions no solution pair variable

A solution of a system of two equations in two variables is an ordered ______ that makes both equations true. [13.1a]

To determine

To fill: The blanks provided in the statement “A solution of a system of two equations in two variables is an ordered _________that makes both equations true.”

Answer to Problem 1VR

Solution:

A solution of a system of two equations in two variables is an ordered pair that makes both equations true.

Explanation of Solution

Given information:

The options are: algebraic, graphical, intersection, union, infinitely many solutions, no solution, pair, variable.

Explanation:

Consider any system of two equations in two variables.

A solution of an equation is the value that will make the equation true. For a system of two equations, there will be two variables. The two equations can be solved and the values of the two variables provided the solution of the system of two equations. The obtained values of the two variables is represented as an ordered pair of values. The ordered pair values makes the system of two equations to be true.

Therefore, the correct fill in the blanks is “pair”.

For example:

Consider the system:

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

Here, the solution of this system is $\left(3,-1\right)$, which is an ordered pair that makes both equations true.