solving systems of inequalities by graphing

In the previous post we have discussed about analyzing equations and inequalities and In today's session we are going to discuss about solving systems of inequalities by graphing. If variables are not equals to each other then we can say it is an inequality. Now we will discuss some of the conditions for an inequality which are: let we have two variables ‘p’ and ‘q’ then:
Condition1: If p ≠ q; that represents ‘p’ is not equals to ‘q’;
Condition 2: If p < q then it represents ‘p’ is less than ‘q’;
Condition3: If p > q then it represents ‘p’ is greater than ‘q’.
If the given conditions are present then we say that inequality is present. Now we will discuss how to solving systems of inequalities by graphing. We need to follow some steps to plot the graph. We know that there are many methods for solving systems of inequalities but solving graphically is the one of the best method. (know more about Inequality, here)
Step 1: To plot graph first we have an inequality equation. Let we have an equation x + y ≤10.
Step 2: Then put the different values of x – coordinate to get the other value of y – coordinate. So we can write the above equation as:
Y ≤- x + 10,
Step 3: If we put the value of x coordinate is ‘1’ then we get the value of y – coordinate is 9.
If we put the value of ‘x’ is 0 then we get the value of ‘y’ is 10. If we put value of ‘x’ is ‘4’ then we get the value of ‘y’ is ‘6’ and we put the value of ‘x’ coordinate is ‘6’ then we get the value of ‘y’ is ‘4’. So we get the ‘x’ and ‘y’ coordinates as: (1, 9), (0, 10), (4, 6), (6, 4). Now we can easily plot the graph of the given inequality. The graph is shown below.



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analyzing equations and inequalities

Before analyzing equations and inequalities first of all it is necessary to know about the equation and inequality. As we know that if equal sign is present in an expression then it is said to be equation. If less than, greater than, less than equal to and greater than equal to operator is present in an expression then it is said to be an inequality. We have to focus on some points to analyzing equation and inequality. Now first of all we will see the properties of equation or (Real number). (know more about Inequality, here)

	Addition	Multiplication
Commutative	P + q = q + p	pq = qp
Associative	(p + q) + r = p + (q + r)	(pq) r = p (qr)
Identity	P + 0 = p = 0 + p	p (1) = p = 1 (p)
Inverse	P + (-p) = 0 = (-p) + p	If p ≠0 then p (1/p) = 1 = 1/p(p)

If we talk about the inequality property then we can write the properties as: For any two real number p and q, one of the given statements is true. p < q, p = q, p > q

Addition and subtraction properties for inequality	For any real numbers p, q and r: 1.      If p > q then p + r > q + r and p – r > q – r 2.      If p < q then p + r < q + r and p – r < q – r
Multiplication and Division property of inequality	For any real number p, q and r: 1.      If  r is positive and p < q then pr < qr and p/r < q/r 2.      If  r is positive and p > q then pr > qr and p/r > q/r 3.      If  r is negative and p < q then pr > qr and p/r > q/r 4.      If  r is positive and p > q then pr < qr and p/r < q/r

If we apply these properties then we can easily analysis the equation and inequality. VSEPR Theory is based on chemistry. The icse guess papers 2013 are useful for the preparation of exam.