Graphical method - Pair of Linear Equations in Two Variables Video Lecture - Class 10

hello friends this video on pair of
linear equations in two variables part
two it's brought to you by exam viacom
no more fear from exam before watching
this video please make sure that you
have watched part 1 so in graphical
method we first draw the graph of both
the equation for example we have this
equation is April a girli plus y is
equal to 5 and 30 minus void 0 1 so
first what we do we draw a graph or
these two I'll explain you how to do
that once we have the graph
now this graph since it is a linear
equation variable first equation and
second house question was only in
equation of torreón it will always be a
straight line linear equations give
straight line now since it's a straight
line if you draw the graph if you have
two straight lines there are three
possibilities one is it will intersect
it will be parallel or a little coin
second
they they are only three possibilities
similarly for these two equations if you
draw the ramp there will be possibility
if you take the lines and try to join
our largest points you need three
possibility either they will be they
will interact then intersect they'll be
parallel or they'll coincide similarly
here also in the lines intersect for
example if you have two equations and
you draw the line for these deepening
and they intersect so if they intersect
that means it has unique solution if the
lines are parallel it has no solution
please make a note of this if parallel
no solution if intersect unique solution
and they have coincident
then they have inside solution let me
write here again this is unique because
we have unique solution here this is no
solution then they are parallel no
spigot see for solution to exist explain
me power remember this and conceal as I
explained
solution is nothing but the point where
both the point likes me sorry if you see
these
nicely and this one only one point so we
can say that this has UNIX function in
this case these two line never be there
is no rating point so we can say there
is no solution correct in this case if
you see both the lines are overlapping
then is there any number of points where
there may be if you see a if all these
points they mean to them so we can say
in this case they are in online solution
please don't mock up things just try to
clear the cancer try to understand why
in case when they intersect they have a
unique solution in case they are
parallel there is no solution they are
coincident they are infinite solution
maybe once again this is a concept if
two lines are intersecting see the
solution is nothing but the point where
both the length sleep but if you have
two lines two equations even trying to
find solution of this I'm trying to find
that common point this satisfies both
the equation
listicles is the equation one and this
is the equation minus of equation one
equation correct my trying to find
solution that is common to both equation
one equation that means I am trying to
find a common point that is there in
line 1 and line 2 so if I am I were to
find one common point that means it has
a unique solution if I'm able to find
infinites all points that is both a
lines of our line that means I can say
they are infinite solutions
if the lines of body will meeting that
means there is no common point where
they're meeting that means there is no
solution I will explain these and taken
examples of all these clear the concept
just try to understand the Mosel
intersecting unique solution because one
point they are intersecting parallel
they are not meeting or together in this
condition if they are coincident they
are overlapping so they're having
infinite solution
infinite number of points they are
correct now let's take an example of
intersect the line thing anything the
same example I think some of boys in
birth in the classes fight boys are more
than girls by one find them their own
performance so let me dig boys VX and
girls my wife
correct now I am told add some boy and
girl is fine that means I can see that X
plus y is going to fight right because
this is the X is the number of boy and
why is it number of birth boy required
girl is right so I guess the X plus y is
will fight this worthless girl is going
to fight also boy is one more than curve
that means boy is one modern girl that
is X minus y is going to do one y
because Y is our bowline birth Bama if
you supply boys to subtract girls from
boys you get one because she looks
opposed it I am saying boys are more
than girls buy one let's of all boys at
10 it does alright so today - I am going
to one similarity heroes of X minus y is
1 to 1
all right please understand this because
if you don't understand these logic you
will not be able to formulate the
equations and then you will not be able
to solve questions this is very critical
but I am saying some of boys and girls
in the class is fine that means boil as
well as fight boys X values Y so I say X
plus y so everyone when I say boy is
more than girls by 1 that means X minus
y is going to 1 all right whatever I can
see there is good boys good with eggs
right endured is going to Y losses boys
up 1 more than good correct
boys are more than girls by 1 so if I
subtract 1 from boil because they are
one extra that's a fragment from right
that means the number of equal I can
also say Expensify 3 2 1
X minus one will do by both are same
actually if you take Y this side with
accomplishments like you interpret the
way you want if you think this is easier
for you
this is number avoid this is number of
nerve since the number of boys why extra
then I subtract one from the boy then
they can say they'll both the quantity
is same so again say X plus y X minus
one squared Y or say writing this
equation will turn out to be a slim
small splitting ball
correct say we have now we have two
equations this equation one in this
individual now since we have two
equation in video sorbets losses in this
slide we are going for the graphical
method so for graphical method the first
step I explained was laundr
okay you will learn to love and then
we'll see if it is intersecting it means
it has unique solution it is parallel no
solution if it's coincident that this
infinite solution first let me put some
values here is 0 this is 1 3 4 5 1 2 3 4
5 correct X plus y is a little bit file
not let me for the equation one or
equation one that we take a table XY
table right so if I put X is equal to 0
in this equation X plus minus 1 Phi X
equal to 0 our code that becomes 0 plus
y is going to find so why become pipes
why is one not any good y is equal to
loosen up ever by the pendulum so this
becomes X plus 0 is going to 5 by
because Y is equal to 0 they come to
explore different so we want to wear
this
let's take more values I put X can do to
let us 2 plus y is going to find so Y is
going to 3 so Y is equal to 3x again
it's many now let me do put wise when
this becomes X plus 3 is equal to 5 so
here X becomes 3
so this is three sixty four points are
more than up actually with three points
over we and autograph so therefore point
P about collocation similarly you try to
plot a graph for equation so let's find
the x values so here what we do let me
put X equal to 1 X Delta 1 I'll get
small equation I'll get 1 minus y is
equal to 1 1 guess the reason why I am
going 0 Delta codex go too long this
becomes 2 minus y is equal to 1 we saw
this this becomes y is going to 1 y
comes here 1 comes here
why it's going to 180 put one more point
if you put a square the 3 3 minus y is
equal to 1 here Y is going to do this
becomes 2 3 how are three points see
points although both is efficient to
prodigal not is project first is 0 comma
5 is this one again is 5 comma 0 is this
point then we have proof ahajni X is 2 y
is 3 and 3 comma 2
this is 2 ways so now i 1 3 4 points i
can this join these points alright if I
join this point what I will get is a
straight line this is straight let me
check it by drawing these points I got a
straight line so this line is nothing
but equation for x plus y is equal to 5
now let me draw equation for x - y - 1
for x minus y squared - 1 x is 1 by 0 X
is 1 by Z at this point X is 2 y is 1
this one X is 3 y is
this one if you know Lord that line is
what we will see that both the lines
intersect both the line in the Sun at
this point and this point is nothing but
X is 3 minus 2 and this is nothing but X
comma Y correct so we can say that X is
equal to 3 and Y is equal to 2 is the
solution for these two equations that
means the number of boy is 3 in the
number of girl is begin a very high on Z
X plus y is going to 5c plus 2 is equal
to 5 and boy is one more than good
because Y is T in the list correct very
simple what we have done the first thing
is we need to understand the problem we
hand this to the problem and go to this
equation X plus y is equal to 5y plus
del 2 5 and y -1 to 1 because the number
of Y is 1 more than a number since we
have this 2 equation we have found the
value of x and wipes which satisfy this
equation we have plotted the graph we
have the graph we found that these steep
ramps these two lines meet at 3 comma
then we can say that X is 3 and Y is
equal to B the solution of this equation
and that's what we want
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