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Solving Systems Of Linear Equations And Inequalities

When we plot a graph then if equation makes a straight line then the equation is known as linear equation. For example:  y = mx + c; where ‘m’ is the Slope of a line and ‘c’ is Y- intercept where the line crosses the y- axis.
When we have two variables and those variables are not equal then we say that there is inequality present in the variables.
For example:  x ≠ y; here ‘x’ is not equal to ‘y’.
Now we will see process of solving systems of Linear Equations and inequalities:
Suppose we have the linear equation 2p + q = 12 and 4p – 3q = 6; solve this linear equation:
Here in this given equation for ‘q’, we cannot solve for ‘p’. so can write the first equation as:
 ⇒ 2p + q = 12;
⇒ q = 12 – 2p; so we find the value of ‘q’;
Now put the value of ‘q’ in the second equation:
On putting the value of ‘q’ in the equation we get:
⇒ 4p – 3q = 6;
⇒ 4p – 3 * (12 – 2p) = 6;
⇒ 4p – 36 + 6p = 6;
Now we add like term;
⇒ 10p = 42;
⇒ p = 4.2
Now put the value of ‘p’ in 1st equation.
⇒ q = 12 – 2p;
⇒ q = 12 – 2 * 4.2;
⇒ q = 3.6;
So the value of ‘p’ and ‘q’ is 4.2 and 3.6;
Now suppose we have -4p < 15; and we have to solve this given inequality.
In the given inequality we divide -4p on both sides of an equation.
⇒ -4p < 15;
Now on dividing -4p on both sides we get;
⇒-4p/-4p < 15/-4;
When we divide 4 by 4 we get one, so in this equation we remain with p;
⇒p < -3.75;
⇒ p > -3.75;
So we can say that the value of ‘p’ is greater than -3.75

Topics Covered in Solving Systems Of Linear Equations And Inequalities

Graphing Systems of Inequalities

Graphing systems of inequalities becomes easier if you know how to plot Linear Inequalities on number line. For instance, we have to graph the system of inequalities given as:
2P – 3Q < 12
P + 5Q < 20
P > 0

Graphing system of inequalities is similar to finding the solution for different inequalities and then plotting the solutions to get the common...Read More

Graphing Systems of Equations

Equation can be defined as an expression which involves equals to symbol. It is necessary in an equation that left hand side of the equation must be equals to right hand side of equation. Equation is also considered as a Mathematical Expression. It involves constants, variables, numerical values, exponential terms and others mathematical terms. It is simila...Read More

Solving Systems of Equations Graphically

To solve a system of Linear Equations in mathematics we have several methods. One such method is Graphing of equations and solving them. This method is better because through this you get the pictorial view of the solution of a system of linear equations. Accuracy has to be maintained in graphing the lines, so that exact values of unknowns are ev...Read More

Cramer's Rule

In mathematics, there are lots of equations which are very complex and difficult to solve. There is a rule for Linear Equations which solves System of Equations in one variable easily and this rule is called as Cramer's Rule and stated as: Method for solving linear equations by use of determinants.

There are some steps which are used in Cramers Rule:

Step 1: First pi...Read More

Solving Systems of Equations in three Variables

Equation can be defined as an expression made of variables and constant terms. Variables are elements which can vary their values but constant terms have a fixed value. Let us see the procedure of solving systems of equations in three variables.

In order to solve linear equation in three variables, we require three Linear Equations. We ...Read More

Application of Linear Programming

Linear Programming method is a crucial concept of mathematics that generally involves solving word problems by Graphing Linear Inequalities. These word problems are similar to the ones we have been studying in Math. Inequalities are formed by collecting necessary information from the problem. If we miss any inequality then solution to the problem may no...Read More

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