Pre-Algebra Demystified

PRACTICE

1. Find the slope of the line containing the two points (
   3, 4) and (6, 8).


2. Find the slope of the line containing the two points (9, 3) and (
   4,
   2).


3. Find the slope of the line whose equation is 5x
   3y¼8.


4. Find the slope of the line whose equation is
   2xþ4y¼9.


5. Find the slope of the line whose equation is xþ7y¼10.

ANSWERS

1.

4

9

2.

5

13

3.

5

3

4.

1

2

5.

1

7

Solving a System of Linear Equations

Two linear equations of the form axþby¼c, where a, b, and c are real
numbers, is called asystemof linear equations. When the two lines intersect,
the coordinates of the point of intersection are called the solutionof the
system. The system is then said to beindependentandconsistent. When the
lines areparallel, there is no point of intersection; hence, there is no solution
for the system. In this case the system is said to beinconsistent. When the two
lines coincide, every point on the line is a solution. The system is said to be
dependent(see Fig. 11-26).
To find a solution to a system of linear equations, plot the graphs for the
lines and find the point of intersection.

EXAMPLE

Find the solution of:

xþy¼ 8

x
y¼ 2

CHAPTER 11 Graphing 225