So here is another terminology. The COORDINATE PLANE and the ordered pairs we just discussed is together known as the RECTANGULAR COORDINATE SYSTEM.

In a rectangular coordinate system the coordinate axes divide the plane into four regions called quadrants. These are numbered counter clockwise with Roman numerals as shown in the Figure below.

As illustrated in Figure it is easy to determine the quadrant in which a given point lies from the signs of its coordinates: a point with two positive coordinates ( + , + ) lies in Quadrant I, a point with a negative x-coordinate and a positive y-coordinate lies in Quadrant II, and so forth

Points with a zero x-coordinate lie on the y-axis and points with a zero y-coordinate lie on the x-axis.

Now remember that the idea of having a number line and that of a rectangular coordinate systems was to describe algebraic statements geometrically and vice versa?? Well, what are these algebraic statements?? They are equations and inequalities. Let's look at the equations and how we can express them GEAOMETRICALLY using the XY-PLANE

Suppose we have the equation

We define a SOLUTION of such an equation to be an ordered pair of real numbers (a, b) such that the equation is satisfied when we substitute x = a and y = b. The SET OF ALL SOLUTIONS IS CALLED THE SOLUTION SET OF THE EQUATION. Here are some examples

Example#1

The pair (3,2) is a solution of

6x-4y=10

since this equation is satisfied when we substitute x = 3 and y = 2. That is

6(3)-4(2)=10

which is true!!

However, the pair (2,0) is not a solution, since

We make the following definition in order to start seeing algebraic objects

geometrically.

Rectangular Coordinate System
So here is another terminology. The COORDINATE PLANE and the ordered pairs we just discussed is together known as the RECTANGULAR COORDINATE SYSTEM. In a rectangular coordinate system the coordinate axes divide the plane into four regions called quadrants. These are numbered counter clockwise with Roman numerals as shown in the Figure below. As illustrated in Figure it is easy to determine the quadrant in which a given point lies from the signs of its coordinates: a point with two positive coordinates ( + , + ) lies in Quadrant I, a point with a negative x-coordinate and a positive y-coordinate lies in Quadrant II, and so forth Points with a zero x-coordinate lie on the y-axis and points with a zero y-coordinate lie on the x-axis. Now remember that the idea of having a number line and that of a rectangular coordinate systems was to describe algebraic statements geometrically and vice versa?? Well, what are these algebraic statements?? They are equations and inequalities. Let's look at the equations and how we can express them GEAOMETRICALLY using the XY-PLANE Suppose we have the equation We define a SOLUTION of such an equation to be an ordered pair of real numbers (a, b) such that the equation is satisfied when we substitute x = a and y = b. The SET OF ALL SOLUTIONS IS CALLED THE SOLUTION SET OF THE EQUATION. Here are some examples Example#1 The pair (3,2) is a solution of 6x-4y=10 since this equation is satisfied when we substitute x = 3 and y = 2. That is 6(3)-4(2)=10 which is true!! However, the pair (2,0) is not a solution, since We make the following definition in order to start seeing algebraic objects geometrically.
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