Graph Systems of Inequalities

Algebra is a subdivision in mathematics in which comprises of infinite number of operations on equations, polynomials, inequalities, radicals, rational numbers, logarithms, etc. Graphing system algebra inequalities is also a part of algebra. It is similar to the graphing of ordinary equations, but here we got to graph the inequality given either greater or less than. In graphing system of inequalities , the area overlapping is the solution set.. The following sections helps us to learn much better about graphing system of inequalities.

Steps to solve system of inequalities:

The steps involved in graphing system of inequalities are as follows,

Consider the inequality y > ax+c
Step 1: Convert the given equation as y =ax+c.
Step 2: Since the given inequality is a function of x, let y =f(x).
Step 3: Therefore f(x) = ax+c.
Step 4: Substitute various values for ‘x’ and find corresponding f(x).
Step 5: Table the values as follows x  &  f(x)  the values of x as -3, -2, -1, 0,1,2,3. and for f(x) their corresponding values.
Step 6: The values in the table are the co-ordinates, graph them.
Step 7: Shade the inequality range above the line, since greater than symbol (>) is given.
Step 8: Shade the inequality range below the line, if less than symbol (>) is given.
Step9: Repeat the same steps for next equation also.
Step 10: Shade the region which is overlapped, which is the solution region for the system of inequalities.


Example problem for graphing inequalities:

Problem 1:

Graph the given system of inequalities and find the solution region,

3x - y < 4

2x + y < 3
Convert the given equation as

y >3x+4
Since the given inequality is a function of x,
Let y =f(x).
Therefore
f(x) = 3x+4.

Substitute various values for ‘x’ and find corresponding f(x).
When x= -3
f(-3) = (-3)3 +4,
-9+4,
-5, therefore the co-ordinates are (-3, -5)

When x= -2
f(-2) = (-2)3 +4,
-6+4,
-2, therefore the co-ordinates are (-2, -2)

When x= -1,
f(-1) = (-1)3 +4,
-3+4,
1, therefore the co-ordinates are (-1, 1)

When x= 0
f(0) = (0)3 +4,
0+4,
4, therefore the co-ordinates are (0, 4)

When x= 1
f(1) = (1)3 +4,
3+4,
7, therefore the co-ordinates are (1, 7)

When x= 2
f(2) = (2)3 +4,
6+4,
10, therefore the co-ordinates are (2, 10)
Tabulate and graph them, and mark the inequality
Following the same procedure for the second equation and graph them. the graph looks like,

On Graphing them combined, we get the solution region as ,

Problem 2:

Graph the system of inequalities

4x +3y <2

2x+y >8

Solution:

Following the above procedure and graphing them, the solution range is as follows,