01 - Intersecting lines (explanation) - Class 10 - Maths Video Lecture

hey everyone
today we are going to learn about pair
of linear equations the basic concepts
and the basic terminologies for
understanding this let us consider the
situation I went to a fruit shop and
bought one mango and one Apple that
shopkeeper charged me 12 rupees for one
mango and one Apple I was coming home
thinking about the individual prices to
find the prices I assumed the price of
one mango the X rupees and price of an
apple VI rupee
so therefore total expense for one mango
and one Apple can be given as X plus y
equal to 12
since I do not know their individual
prices I can assume many values for x
and y which gives me total of 12 like if
I assume the price of one mango is 3
rupees then price of Apple has to be 9
the piece so that the total becomes 12
if I assume the price of mango as 2
rupees then price of Apple has to be 10
rupees so that the total comes out to be
12 similarly if I assume the price of 1
mango is 4 point 5 apiece then for Apple
it has to be 7 point 5 rupees which
gives us total of 12 like that I can go
on checking for different values since
the Rileys for x and y are varying from
time to time they are called as
variables and we can see the equal to
sign over here which shows that left
hand side values and that insert values
are equal therefore this mathematical
expression is called last equation now
we have the equation X plus y equal to
12 we can see that there is nothing in
the power that means there is a power of
1 when powers of the variables in the
equation are one that equation is called
as linear equation now you must be
thinking why this equation is called as
linear
linear means straight such equations
where powers of the variables are one
they give straight lines but how do we
know that this equation gives a straight
line for understanding that let us take
help of these values which we are
assumed for this equation X plus y cos
of 12 so for that we have to use the
ground so here is the graph first value
we have assumed is X is 2 rupees and Y's
10 rupees so X is 2 y is 10 this is the
point and next value we assumed is x
equals to 3 rupees and y equals to 9
rupees so X is 3 and Y is 9 so point is
over here and the next value we have
assumed is X is 4 point 5 rupees and y
is 7 point 5 rupees so the point is here
so we have plotted all the three points
let us join them so from this we can see
that we are getting a straight line so
from here we can conclude that whenever
the powers of the variables of the
equation is 1 that equation gives us
straight lines and therefore they are
called as linear equations we have we
need to note that we have some equations
like X equal to 4 this equation have
only one variable that is X and power of
this variable is 1 let's see what the
graph says about this equation so here
is a graph and this line passes through
the point 4 on the x-axis this line is
parallel to Y axis just because for
every value of y we have value of x as 4
and since this equation gives a straight
line it is called as linear equation
let's consider one more example like y
equals to 7 here again we can see that
there is only one variable Y and power
of variable is 1 so let's see what the
graph has to say about this equation so
here is the graph this line passes
through the point 7 on the y-axis and
this line is parallel to x axis just
because for every value of x we have
value of y and 7 so this gives straight
line so therefore it is called as linear
equation so from this we come to know
equations like X equal to 4 and y equal
to 7 are also called as linear equations
we can take this as node number 1 now
node number 2 there are some equations
like X square equals to 4 or X square
plus y square equals to 2 etc here we
can see that powers of the variables are
more than 1 so therefore when powers of
the variables are greater than 1 then
such equations are not called as linear
equations but still I have to find the
value of one mango and the value of 1
Apple so this time I have sent my
brother to the same shot he bought two
mangoes and one Apple for 17 rupees as
they have already assumed the price of
one mango has X rupees and price of 1
Apple as wire rupees we can write this
as 2x that is 2 mangoes plus 1 Apple and
total expenses 70 rupees we can see that
here we got one more linear equations
since the powers of the variables are 1
so for finding the value of x and y we
have to deal with two equations one is x
+ y it goes to 12 and second is 2 X plus
y equals 270
since we are dealing with two linear
equations we can say that we are dealing
with pair of linear equations for
finding the values of the variables we
need to note one point is that number of
equations we have should always be
equals to number of variables here we
have two equations and we have to find
the values of two variables that is X
and y
solving the linear equations means
finding the values of x and y we have
already seen the graph of x + y 4 - 12
now we have to see the graph for this
equation for that we require some values
for x and y so let us assume some random
values let us say if X is 3 then it is x
2 to 3 so 6 then Y has to be 11 so that
total becomes 17 let us assume one more
value if I say X is 4 then it is x 2
2008 then value of y has to be 9 so that
total becomes 17 so now we have two set
of values for X and y1 is X is 3 y is 11
and other one is x equals to 4 y equals
to 9 let's see how this graph looks like
here is a graph here you can already see
a line for the equation X plus y was it
well now we have to draw a line for 2x
plus y which is 17 and we have assumed
some values like X is 3 rupees then Y is
11 rupees so X is 3 y is 11 point is
here and the next point is X is 4 rupees
y is 9 rupees so point is over here so
after joining them we get the second
line that is for the equation 2x plus y
equals 270 here again you can see we got
a straight line because it was a linear
equation these two lines are
intersecting at point five seven and we
take the point of intersection as the
solution so therefore x equals to 5 that
is price of one mango is 5 rupees and y
equals to 7 that is price of one Apple
is seven rupees
this method of solving linear equations
is called graphical method
in graphical method we get three types
of questions questions for intersecting
lines questions for coincident lines and
questions for parallel lines the
question which we are solved for price
of one mango and price of an apple is of
intersecting lines type because those
two lines were intersecting and these
two we are going to learn in the next
session so for intersecting lines you
always get only one solution that is the
point of intersection which is also
called as common point that solution is
always unique and for the linear
equations for which we get the solution
those linear equations are called as
consistent linear equation
so in this session we have learned
you