03 - Coincident Lines (explanation) Video Lecture - Class 10

let's move into the third chapter of
class 10th which is pair of linear
equation in two videos in previous class
we have seen linear equation two
variables however we dealt with one
linear equation of two variable here we
will deal with two equations two linear
equations in two variables together in
this video we'll talk about intersecting
coincident and parallel lines in short
while we come to know what are
intersecting lines
what with coincident lines and modern
all our lines generated through pair of
linear equations in two variables here I
have three sets of linear equations in
two variables x and y x and y XY XY XY x
one degree of all these equations
highest degree of all this equations is
1 so there are linear equations now this
one here X minus 2 y is equal to 0 3 X
plus 4 y is equal to 20 now if I write
this equation X minus 2 y equal to 0
like this minus 2 y is equal to minus X
X the other side - - cancelled Y would
be equal to 1 over 2 X or x over 2 same
operation I do with this one this is 3 x
+ 4 y equal to 24 y equals to 20 minus 3
X Y would be 20 minus 3x over 4 so I
have this equation I have a solution now
let's put some values of x in both the
equations and get Y values I have these
two equations here X minus 2 y is equal
to 0 3x minus 4y equals 220 now this is
question gave me Y is equal to x over 2
and this equation gave me Y is equal to
22 minus 3x over 4 now let's take some x
values here which will give me Y value
from this equation
and why value from this equation so
these Y values I will call them y1 these
Y values I'll call them Y - let's take
some X values here I have taken the
smaller values 0 1 2 3 4 5 for X now in
this equation here I'll replace X with
all these values which will give me Y
values if I replace X with 0 it will
give me 0 over 2 which is 0 if I place X
with 1 here it will give me Y as 1 over
2 which is 0.5 when X is 1 Y is 0.5 when
X is 2 y is 1 when X is 3 y is 1 point 5
when X is 4 y is 2 when X is 5 y is 0.5
you can see here this line started from
here and grew up to this point here
likewise if I replace here X with all
these values I'll get some Y values here
from this equation when x is 0 Y 2 which
file I replace this X with 0 it will
give me Y is 5 20 minus 3 into 0 & 0 20
minus 0 is 0 when you work for me give
you 5 when X is 1 this Y is 0.25 you can
see this line this orange line is for
this y 2 already started XS 2 y is 3
point 5 X is 3 y is 2 point 7 5 started
from here gradually it is glowing and XS
for y is 2 y is 2 when X is 5 y is 1.25
so for these five X values from this
equation I got these Y values from the
same X values from this equation I got
these Y values this blue line
representing y1 is orange line
representing these values by 2 now in
this blue line and orange line let's
highlight
of the coordinates I write the name of a
question on this blue line this orange
line here representing three years minus
4y equals 220 you can see this blue line
on this orange line both these lines are
intersecting at this point here which is
X is 4 and Y is 2 here and mention this
point here where X is 4 and Y is 2 so
these kind of lines where both the lines
are intersecting at some point those
type of lines are called intersecting
lines now let's try to understand what
do you mean by these intersecting lines
or want to be interpret by this point of
intersection where these two lines are
intersecting we had these two equations
gave me intersecting lines and the point
of intersection balls to means X was 4
and y was two in these two equations
which gave me intersecting lines at
these two points where X was 4 and y was
two if I replace X in this equation here
with 4 and Y with 2 like this X is 4 and
Y is 2 4 minus 4 equals to 0 this is my
left hand side and this is right inside
both are equal let's replace 4 & 2 in
this equation also 3 into 4 plus 4 into
2
it was 2 20 24 is 12 or in 2 is 8 plus
20 20 plus the 20 means left and side is
equal to right hand side now the
interpretation of intersecting lines the
point of intersection here X is 4 y is 2
the value which we get is the unique
value for is the unique value for X 2 is
a unique value for y why do we call it
unique is only X equal to 4 and Y is
equal to 2 will make my equation equal
to left hand side and right hand side
left hand side and guidance on in this
equation here right hand side is 0 here
that inside is 20 we wanted some value
for x and y which can make this equation
equal to right hand side which is 0 same
is applicable to this equation we wanted
some value for x and y which can get me
20 which is the right hand side value
and the condition is in both the
equations value for X and value for y
should remain common means whatever
value I keep here for X same value I
have to put here for X whatever value I
put here for Y same value I need to put
here for y also these two other values
which I got on the point of intersection
from those two intersecting lines x
equal to 4 y is equal to 2 these are the
only two values which will make my
equation equal to left hand side to
right hand side left hand side to right
hand side if you take any other value
for x and y those might equate left hand
side and right hand side for one of the
equations but those same values we
not equate second equation let's try
with some other value of X X is say 2
and y is 1 X minus 2 y equal to 0 X is 2
y is 1 minus 2 equal to 0 this equation
left-hand side is 0 right hand side if
you done let's try this would be the
question 3 into 2 3 into X plus 4 into Y
which is 1 equals 2 26 plus 4 is not
equal to 3 10 if not equal to 20 means
left hand side is not equal to right
hand side mean this value is not the
unique value for this equation that is
why we look for the value which we get
from the point of intersection vomiter
setting lines those values are a unique
values which will make both the
equations equal to left hand side and
right hand side left hand side and right
hand side other than these two values
there is no other value which can equate
left hand side and right hand side left
and send that inside for both equations
together now let's try for this equation
here this will be 2y equals 2 over minus
X Y would be 4 minus x over 2 this one
here would be 4y equals to 12 minus 2x
so Y would be 12 minus 2x over 4
question number 1 question number 2 y is
equal to 4 minus x over 2 y is equal to
12 minus 2x over 4 these two other
questions here I have these X values
here I replace this X with these X
values which will get me Y values okay
when X is 2 y is 1 X is 3 y is 0.5 X is
5 y is 0 point 5 negative now let's take
these x values and put them here in
place of X in this position now I have
these two lines orange one representing
y2 blue one representing y1 now in y1 it
is the line when x is 0 Y is 2 x is 0 Y
is 2 here X is 1 Y is 1.5 X is 1 year Y
is 1.5 this point here the X is 2 y is 1
X is 2 y is 1 this point here
likewise when X is 5 y is negative 0.5
when text is 5 years Y is negative 0.5
this is negative 0.25 so X is 5 y is
negative leader of 1 5 same is with this
line when x is 0 Y is 3 the blue line is
x + 2 y equal to 4 orange line is 2x + 4
y equal to 12
now these two lines here they are not
intersecting these two lines are
parallel lines means if you stretch both
the lines on both the ends till whatever
lengths you like these two lines will
never intersect now what do you mean by
these two parallel lines which we have
got from these two equations the blue
one for this equation
arrangement from this equation from
these two equations we got color lines
this equation gave me a line this
equation give me a line and both the
lines from these two equations were
parallel so we call it angle lines
equation
parallel lines equation now since they
were parallel lines it means they will
never touch each other given level our
teachers it means they will never be a
common point for for these lines now in
case of intersecting lines we have
common points X common for both the
questions why common for both equations
which ultimately gave me left-hand side
equal to right hand side left hand side
equals to right hand side for both the
equations however in case of parallel
lines since there is no common point it
means there will not be any common
solution means there is no common value
for X there is no common value for Y
which would equate left hand side equal
to right hand side left hand side equal
to right hand side for both the
equations that's the interpretation of
our lines means equations which gave me
all aligned x' do not have any common
solution now let's look into this
equation here now let's put this into
this further three y equal to line minus
2 X so Y is equal to 9 minus 2x over 3
so this will be y is equal to 18 minus
4x or 6 same I'll take some x value here
I have these X values let's replace this
X here with these values and get some Y
values 3 gave me 1 till 5 I have these
many values let's look like this X with
these X values x is 0 Y is 3 X is 1 Y is
2 point 3 3 XS 2 y is 1 point 6 7 you
can see this is the orange line
representing this Y to this line started
at the same point where this line y1
started w1 and running all the same line
means orange line is running exactly on
top of the blue line let's see X is 3 y
is 1 he can see my blue line has been
completely covered by this orange line
interpretation of this superimposing or
both the lines sitting on top of each
other is we saw that these two equations
or this pair of linear equation gave me
for incident lines right it coincident
lines : tenant lines means both the
lines are running on top of each other
or both the lines are superimposing each
other means whatever value we got for
mine in this equation here
those values and whatever values we got
here for y1 see he can see here for text
value y 1 is 3 y 2 3 4 1 which is X Y 1
y 2 Allah seen here that's the reason
this line here is coincident or both the
lines have superimposed each other now
the reason for this to happen is if you
look at this equation here and this
equation here both the equations are
actually seen if you multiply both sides
of this equation by 2 you will get this
equation y 2x + 3 y x 2 gives you 4x
plus 6y 9 x 2 gives you 18 all if you
divide both the sides of this equation
by 2 you will get this equation 4x plus
6y divided by 2 gives you 2x + 3 1 18
divided by 2 gives you 9 that is the
reason behind these two equations giving
you foreign lines now como insulin lines
have all the points in common
not like intersecting lines where only
one point
or not like parallel lines where none of
the flights were coming here all the
points are common means whatever x and y
value equates left-hand side and
right-hand side of this equation same
value of x and y will equate left-hand
side and right-hand side of this
equation also now their way around
whatever x and y value equate left-hand
side and right-hand side of this
equation same x and y value will equate
left-hand side and right-hand side of
this equation also and you know that in
linear equation you can have a number of
Y values from given X values means all
those pairs of X&Y satisfying one of the
equations will definitely be satisfying
second equation means left-hand side
equal to at inside
left-hand side equals to right-hand side
that Center predation of coincident
lines