Hello friends today we are going to discuss about Linear equations, inequalities which you need to study in grade XII of every education board .As you all know about solving linear equations and you all studied them in grade X and XI. Linear equation is a equation which have 1,2 ,3 or more than that unknown variables with some known variable.
Linear equation in one variable: This type of equation has only one solution or you can say unique solution.
Example: 3X+5=14
3X=9 or X=3
These equations are very simple to solve you just need to put x one side and other values on other side and u can easily get the desired result.
Linear equation with two variable: any equation is in the form of aX+bY+c=0 is called linear equation with two variable .where a,b,c are real numbers and X,Y are variables .For solving this type of equations we need to have 2 equations because we are having two unknown variable in the form of X,Y.
Example: 2X+3Y=15&3X+3Y=18
Now solving this type of equation we need to we need to add or subtract both the equation if sign are same then subtract them and if not same than just add them.
Now in above case we need to subtract on subtraction we will get X=3 and then put this value in above equation to find the value of y .than you will find the value of y is 3.
Note-in above example sign and number before variable are same so the problem solved easily but
if the number before the variable are not same than u need to multiply them by a constant. This constant you have to decide by your own.
Now we will discuss about the inequalities
Inequalities are basically linear equation type problem just the change is that you can change the sign according to inequalities but you can’t change sign in linear equation that is the basic difference between them. For solving inequalities you need to fallow fallowing steps
*Add or subtract both the number same side.
*On switching change the sign of inequalities.
*Multiply and Divide by same positive number
*if you Divide by negative number or multiply by positive number then you need to change the sign of inequalities. It will be more clear when we go through the examples.Know more about inequality here,
Example: Solve this inequality
5X+4>-10X+14
Step one add or subtract same value
5X+4-4>-10X+19-4
5X>-10X+15
5X+10X>15
15X>15
X>1
In this way just fallowing simple steps we can solve inequalities problem easily.
Example: solve this inequality
4X<16
Divide by 4 each side you can easily solve this problem
X<4
Now the example given blow is taken from compound inequality .These are complicated problems .Let us see one problem .
Example:3X+9>18 and 4X-7<-11
Now for that type of problem you just need to take both the problems one by one and them just combine them.
3X>18-9
3X>9
X>9
And
4X<-11+7
4X<4
X<1
Now answer of the problem will be the combination of both that will be X>9,X<1 by this you can say all the number above 9 and blow 1 are the solution of this equation.
We have discussed about linear equation and inequalities,Inequalities are little difficult to solve so you need to practice a lot and to know answers of interesting questions like can a rational number be negative wait till next session and You can also refer grade XII blog for further reading on Formal/informal proofs.Read more maths topics of different grades such as Correlation and causation in the next session here.
Linear equation in one variable: This type of equation has only one solution or you can say unique solution.
Example: 3X+5=14
3X=9 or X=3
These equations are very simple to solve you just need to put x one side and other values on other side and u can easily get the desired result.
Linear equation with two variable: any equation is in the form of aX+bY+c=0 is called linear equation with two variable .where a,b,c are real numbers and X,Y are variables .For solving this type of equations we need to have 2 equations because we are having two unknown variable in the form of X,Y.
Example: 2X+3Y=15&3X+3Y=18
Now solving this type of equation we need to we need to add or subtract both the equation if sign are same then subtract them and if not same than just add them.
Now in above case we need to subtract on subtraction we will get X=3 and then put this value in above equation to find the value of y .than you will find the value of y is 3.
Note-in above example sign and number before variable are same so the problem solved easily but
if the number before the variable are not same than u need to multiply them by a constant. This constant you have to decide by your own.
Now we will discuss about the inequalities
Inequalities are basically linear equation type problem just the change is that you can change the sign according to inequalities but you can’t change sign in linear equation that is the basic difference between them. For solving inequalities you need to fallow fallowing steps
*Add or subtract both the number same side.
*On switching change the sign of inequalities.
*Multiply and Divide by same positive number
*if you Divide by negative number or multiply by positive number then you need to change the sign of inequalities. It will be more clear when we go through the examples.Know more about inequality here,
Example: Solve this inequality
5X+4>-10X+14
Step one add or subtract same value
5X+4-4>-10X+19-4
5X>-10X+15
5X+10X>15
15X>15
X>1
In this way just fallowing simple steps we can solve inequalities problem easily.
Example: solve this inequality
4X<16
Divide by 4 each side you can easily solve this problem
X<4
Now the example given blow is taken from compound inequality .These are complicated problems .Let us see one problem .
Example:3X+9>18 and 4X-7<-11
Now for that type of problem you just need to take both the problems one by one and them just combine them.
3X>18-9
3X>9
X>9
And
4X<-11+7
4X<4
X<1
Now answer of the problem will be the combination of both that will be X>9,X<1 by this you can say all the number above 9 and blow 1 are the solution of this equation.
We have discussed about linear equation and inequalities,Inequalities are little difficult to solve so you need to practice a lot and to know answers of interesting questions like can a rational number be negative wait till next session and You can also refer grade XII blog for further reading on Formal/informal proofs.Read more maths topics of different grades such as Correlation and causation in the next session here.
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