Determining whether An bespeak Pair is a equipment of a mechanism of Equations

In Solving straight Equations and Inequalities we learned exactly how to solve linear equations v one variable. Remember the the systems of an equation is a value of the change that makes a true statement as soon as substituted right into the equation.

You are watching: Tell whether the ordered pair is a solution of the linear system

Now us will job-related with systems of straight equations, 2 or much more linear equations grouped together.


System of linear Equations

When 2 or much more linear equations are grouped together, they type a mechanism of linear equations.


We will emphasis our work below on equipment of two straight equations in 2 unknowns. Later, you may solve bigger systems of equations.

An instance of a device of two linear equations is presented below. We use a brace to show the two equations are grouped with each other to kind a system of equations.

(eginarrayc2x+y=7hfill \ x-2y=6hfill endarray)

A straight equation in two variables, choose 2x + y = 7, has an infinite variety of solutions. Its graph is a line. Remember, every point on the heat is a solution to the equation and every solution to the equation is a suggest on the line.

To resolve a mechanism of two straight equations, we want to uncover the worths of the variables the are services to both equations. In other words, we are searching for the ordered pairs (x, y) the make both equations true. This are referred to as the solutions come a system of equations.


Solutions the a mechanism of Equations

Solutions that a device of equations are the values of the variables the make every the equations true. A solution of a device of two straight equations is represented by an bespeak pair (x, y).


To identify if an notified pair is a solution to a mechanism of 2 equations, us substitute the values of the variables right into each equation. If the bespeak pair provides both equations true, the is a solution to the system.

Let’s think about the mechanism below:

(eginarrayc3x-y=7hfill \ x-2y=4hfill endarray)

Is the notified pair (left(2,-1 ight)) a solution?

*
*
*

(−4, −3) does not make both equations true. (−4, −3) is a solution.


This write-up has been modified from "Solve solution of Equations by Graphing," by OpenStax, primary school Algebra, CC through 4.0. Download the post for complimentary at http://cnx.org/contents/0889907c-f0ef-496a-bcb8-2a5bb121717f
3.11.

This modified post is license is granted under a CC BY-NC-SA 4.0 license.


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