L2 : Linear Equation - Linear Equation in one Variable , Maths, Class 8 Video Lecture

hence this video on linear equations in
one variable part two is brought to you
by exam p.m. no more fear from exam so
now let us try to understand what
exactly is linear equation in one
variable because that is what we are
going to deal with in this lesson now as
the name says linear equation linear
equation means why is this equation
linear because the highest power of the
variable in this equation is one so what
do we mean by that selects take an
example so let's take this example 4x
plus 2 is equal to 35 so here what
happens the highest power of this
variable that is X so here when you look
at the variable which is the variable
that is X and what is the power of the
variable in this case the power of the
variable is 1 do we have any other
variable known so that means the highest
power of the variable in this equation
is 1 let us look at few more examples so
let us take this example 5 by 4 into X
minus 4 is equal to 0
how many variables do we have 1 that is
X what is the highest power of X that is
1 so here also the highest power of the
variable is 1 so this is also a linear
equation let's look at yet another
example X square plus y square is equal
to 1 so in this case how many variables
do we have we have two variables that is
X and Y and what is the power of the
variable for X also it is 2 for Y or so
it is 2 so which is the highest power of
variable in this equation that is - so
is this a linear equation no this is not
a linear equation similarly if you look
at this example X to the power 5 minus
2x is equal to 1 so here you have only
one variable X but at this place it has
1 but at this place the power is 5 so
which is the highest power of variable
in this equation that is 5 so is it a
linear equation not again
now if you look at this example 1 plus Z
buying 1 minus y is equal to 40 so here
you have two variables y and z and the
highest power involved is 1 therefore
this is again a linear equation so like
this we can decide whether a particular
equation is a linear equation or not now
when we say linear equation in one
variable that means that equation should
have only one variable for example here
this equation has one variable this
equation also has one variable this
equation has two variables anyways it is
not a linear equation but it doesn't
have one variable also similarly this
equation is a linear equation but this
is not in one variable it has two
variables Y and set so in this lesson we
are only going to talk about equations
which are linear as well as which
involves only one variable so now the
next important task that comes into
picture is solving a linear equation now
what do we mean by something a linear
equation it is about finding out the
values of the variables for which the
left-hand side and the right-hand side
would be equal so those values of
variables are called solutions of that
equation and by finding out those values
we say that we are solving a linear
equation so let us take an example so
let us take let us say we take this
linear equation 4x plus 2 is equal to 35
right so this side is LHS and this side
is RHS right now this LHS because for
our ages the value is 35 which is going
to remain constant for always but for
left hand side the value of x is not
known but there will be certain value of
x for which the left hand side will be
equal to a right hand side because the
question is told or the equation itself
says that the value of x should be such
that this relation holds true right so
how will you solve this equation so now
whatever we do in order to find the
value of
we always need to ensure that at every
step IHS should remain equal to RHS so
let us say so if we want to subtract
something add something we have to do it
on both sides so that the balance is
maintained right so here what we do is
let's subtract 2 from both sides now
what happens now let's say that if on
one side we had 180 Apple the other side
also we have hundred kg Apple if we want
to make we want to ensure that on both
sides happens should be hundred kg if
you are reducing 2 kgs from one side you
will also have to reduce to take this
from the other side it is just like that
so here subtracting from both sides what
happens this becomes 4 X plus 2 minus 2
and this becomes 35 minus 2 so here plus
2 minus 2 cancels out so we get that 4 X
is equal to 35 minus 2 so 35 minus 2 is
nothing but 33 so we got the value of 4
X but we want the value of X so for that
what we can do is divide by 2 divide by
4 on both sides again when you are
dividing on both sides the Equality is
maintained so what happens 4 X 5 4 is
equal to 33 by 4 so therefore what
happens X is equal to 33 by 4 so we are
able to find out the value of x for
which this equation holds true so X is
equal to 30 3 by 4 is the solution for
this linear equation so this is how we
found out the value of x now if you want
to verify that okay is it true that if
we put the value of x as 33 by 4 in this
equation that the relation will hold
true so let us try to do that so let us
put X in NHS so the left hand side will
become equal to 4 into 33 by 4 plus 2 so
that will be 33 plus 2 which will be
equal to 35 and 35 is nothing but R it
is so that means by putting this value
of x we can see that NHS is equal to
ohso therefore this is the right
solution for this linear equation thank
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