1. CONGENIALITY LINEAR EQUATIONS SYSTEM IN TWO VARIABLES

2. THE SOLUTION OF SYSTEM ABOVE BY THE FOLLOWING METHODS GRAPH

3. THE SOLUTION OF SYSTEM ABOVE BY THE FOLLOWING METHODS SUBSTITUTION

4. THE SOLUTION OF SYSTEM ABOVE BY THE FOLLOWING METHODS ELIMINATION

5. SOLVED AND PROBLEMS

Recalling when we found the point of intersection of the lines ax + by = c and px + qy = r then we found coordinates of point of intersection, thet is finding x and y, by manipuating both of equations :

ax + by = c px + qy = r

It is said that both equations above form a linier equations system in two variable, while each equations is called linier equation in two variables.

We use the teminology linier since each of equation above represents a straight line in cartesian coordinates, while two variables mentioned are x and y.

These two variables might represent anything, such as ages, the number of any goods, the amount of money, the electric resistancies of conductors, etc.

And we may replace the leters x and y by any other symbols when necessary.

Finding solution of a linier equations system in two variables as above means finding the values of both variables that stisfy each equation in that system. Or in other words, finding point of intersection of the two straight lines represented by the system of equations.

So here we shall repeat our methods in determining the point of intersection of two straight lines.

And as additions, we shall name our methods and make various applications.

Now consider the following linier system.

7x + 6y = 84 (i) x + y = 13 (ii)We shall find the solution of

system above by the following methods.

Show the solution of system by graph

x + y = 8y = x + 4

X

Y

x + y = 8x = 0 0 + y = 8 y =

8

3x + 2y = 6

y = 0 3x + 2.0 = 6

3x = 6 x = 2

(0,8)