Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable. We will now study methods of solving systems of equations consisting of two equations and two variables. Represent the Cartesian coordinate system and identify the origin and axes.

Systems of Equations and Inequalities In previous chapters we solved equations with one unknown or variable.

We will now study methods of solving systems of equations consisting of two equations and two variables. Represent the Cartesian coordinate system and identify the origin and axes. Given an ordered pair, locate that point on the Cartesian coordinate system.

Given a point on the Cartesian coordinate system, state the ordered pair associated with it. We have already used the number line on which we have represented numbers as points on a line.

Note that this concept contains elements from two fields of mathematics, the line from geometry and the numbers from algebra.

Rene Descartes devised a method of relating points on a plane to algebraic numbers. This scheme is called the Cartesian coordinate system for Descartes and is sometimes referred to as the rectangular coordinate system. This system is composed of two number lines that are perpendicular at their zero points.

Perpendicular means that two lines are at right angles to each other. Study the diagram carefully as you note each of the following facts. The number lines are called axes. The horizontal line is the x-axis and the vertical is the y-axis.

The zero point at which they are perpendicular is called the origin. Positive is to the right and up; negative is to the left and down. The arrows indicate the number lines extend indefinitely. Thus the plane extends indefinitely in all directions.

The plane is divided into four parts called quadrants. These are numbered in a counterclockwise direction starting at the upper right. Points on the plane are designated by ordered pairs of numbers written in parentheses with a comma between them, such as 5,7.

This is called an ordered pair because the order in which the numbers are written is important. The ordered pair 5,7 is not the same as the ordered pair 7,5.

Points are located on the plane in the following manner. First, start at the origin and count left or right the number of spaces designated by the first number of the ordered pair. Second, from the point on the x-axis given by the first number count up or down the number of spaces designated by the second number of the ordered pair.

Ordered pairs are always written with x first and then y, x,y. The numbers represented by x and y are called the coordinates of the point x,y. The first number of the ordered pair always refers to the horizontal direction and the second number always refers to the vertical direction.Watch video · Sal is given a graph and he analyzes it to find the two-variable inequality it represents.

Fit an algebraic two-variable inequality to its appropriate graph. If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *pfmlures.com and *pfmlures.com are unblocked. Write a compound inequality that the graph could represent. Download png. Ask for details A compound inequality contains at least two inequalities that are separated by either "and" or "or".

[-1, 3) The graph of the compound inequality represents the intersection of the graph of the inequalities. 0 votes 0 votes Rate! Rate! Thanks /5(4). Write a compound inequality that the graph could represent. Download png. Ask for details A compound inequality contains at least two inequalities that are separated by either "and" or "or".

[-1, 3) The graph of the compound inequality represents the intersection of the graph of the inequalities.

0 votes 0 votes Rate! Rate! Thanks /5(4). Properties of equalities Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign.

Feb 02, · Learn how to write the inequality given a graph on a number line. To do this we will need to know the difference between open and closed points as well as what it means for a value to be less than or greater than another value.

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