2. Jens
Martensson
SOLVING SYSTEMS OF
LINEAR EQUATIONS
USING GRAPHICAL
METHOD
In this lesson, you will be able to …
2
⮚ Solve system of
linear equation in two
variables by graphing
3. Jens
Martensson
For two equations, a common solutions of the equations is called a
SOLUTIONS OF THE SIMULTANEOUS EQUATIONS.
The solution of the simultaneous linear equations x + 2y = 7 and
3x – 2y = 5 is the point (3,2).
Example:
Solve the system of equations x + y =
1 and x + 2y = 3 by graphical method.
x -2 0 1
y
x + y = 1
x + 2y = 3
x -2 1 3
y
3 1 -1
2.5 1 0
The solution of the simultaneous
equation is, x = -1 and y = 2.
4. Jens
Martensson
We an classify a system of two linear equations by the number of solutions.
Consistent System
Independent System
Dependent System
has one solution
has infinite solution
Inconsistent System has no solution
CONSISTENT SYSTEM OF EQUATION
A system of equations that has at least one solution.
INCONSISTENT SYSTEM OF EQUATION
A system of equations that has no solution.
5. Jens
Martensson
We summarize our lesson of classifying systems of equation with the following:
INTERSECTING LINES
Single solution at the point of intersection.
Consistent and Independent.
OVERLAPPING LINES
Infinite number of solutions.
Consistent and Dependent.
PARALLEL LINES
No solution.
Inconsistent.
6. Jens
Martensson
The system is consistent (it has a solution).
The equations are independent.
The system has one solution which is (1,-2).
x -1 0 1
y
x -1 0 3
y
7. Jens
Martensson
The system is inconsistent (no solution).
The system has no solution.
The system is consistent (it has a solution).
The equations are dependent.
The system has an infinite number of solutions.
x -1 0 1
y
x -1 0 3
y
x -1 0 1
y
x -1 0 3
y
