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Example - Pair of Linear Equation in Two Variable Video Lecture - Class 10
FAQs on Example - Pair of Linear Equation in Two Variable Video Lecture - Class 10
| 1. What is a pair of linear equations in two variables? |  |
Ans. A pair of linear equations in two variables is a set of two equations that involve two variables and have a degree of one. These equations can be represented graphically as two straight lines and can be solved simultaneously to find the values of the variables that satisfy both equations.
| 2. How can we solve a pair of linear equations in two variables? | |
Ans. There are multiple methods to solve a pair of linear equations in two variables. One commonly used method is the substitution method, where we solve one equation for one variable and substitute it into the other equation. Another method is the elimination method, where we manipulate the equations to eliminate one variable and solve for the other. Graphical method and matrix method are also used to solve linear equations in two variables.
| 3. Can a pair of linear equations in two variables have more than one solution? | |
Ans. Yes, a pair of linear equations in two variables can have three types of solutions:
1. Unique Solution: When the two lines representing the equations intersect at a single point, the system has a unique solution. This means that there is only one set of values for the variables that satisfy both equations.
2. No Solution: If the two lines representing the equations are parallel and do not intersect at any point, the system has no solution. This means that there are no values for the variables that satisfy both equations simultaneously.
3. Infinite Solutions: When the two lines representing the equations coincide or overlap, the system has infinitely many solutions. This means that any point on the line represents a solution, and there are infinitely many values for the variables that satisfy both equations.
| 4. How can we graphically represent a pair of linear equations in two variables? | |
Ans. To graphically represent a pair of linear equations in two variables, we plot the points that satisfy each equation on a coordinate plane. The two lines are then drawn connecting these points. The point of intersection (if it exists) represents the solution to the system of equations. If the lines are parallel, there is no solution, and if the lines coincide, there are infinitely many solutions.
| 5. What is the significance of solving a pair of linear equations in two variables? | |
Ans. Solving a pair of linear equations in two variables has various applications in real-life scenarios. It helps in finding the values of unknown quantities, determining the break-even point in business, analyzing supply and demand, optimizing resources, and solving problems related to distance, speed, and time. The ability to solve these equations enables us to make informed decisions and solve complex problems in different fields such as economics, engineering, and physics.
Text Transcript from Video
hello friends this video paid off linear
equations in two variables part 18 is
brought you by exam fear calm no more
fear from exam before watching this
video please make sure that you have
washed videos part 1 - part 17 for
example two men and five two women and
five men can together finish work in
four days three when Hoover and six
pension finishings three days fine time
taken by one man alone and also by one
man let's write whatever is written here
two women and five men they take four
days also three women six men they take
three days we have to find nine taken by
one man to finish the book so let's
assume let's assume that this man does
xqe of work reading X unit of work per
day let's assume this women does exeunt
per day because women was first and men
does why you read buddy right that is
unique per day you need to work per day
this guy is doing X you need work party
this lady and this guy is doing while it
work now since they are taking four and
three days I can assume that total
working stuff
big double total work total over his
winter I can take any value is the best
way to solve this questions is you can
take the W to be LCM of these values and
tell you why because you could take the
LCM of this values it cuts until if I
first see if this guy is the woman is
doing X need of work party and the man
is doing y unit of all party since the
women is taking Ted to women so per day
work done by women is 2x because their
two women
and per day world in my - bye-bye
because there are five men in first case
this forever and they are taking four
days this is total about them you says
nothing but in second case per day work
them maybe minus 3x while because they
are three women per day work done by
minus six why why because they are six
men and the total time taken is three
days this is over I can take W has to be
any well doesn't matter
you simply my my question what I do I am
they W to be LCM of this because
whatever number I take still cut this
will divide by four to every three so
I'd take that would to be twenty thus
for my convenience I can take 24 also
getting any value but if I take twelve
ready for anything that divides both for
entry that this easy for real is because
this will divide and I will get a
simpler equation so I will take it to
individual and here also I take the
equation I get is because this four is
gone now and three is again haircut so I
will get 2x plus 5y is equal to 3 that
is first equation and 3x plus 6y four is
second division now let's solve it so
let me divide multiply this whole thing
by 3 and this by 2 because in this case
both will have 6 accelerate cancel so I
will get 6x plus 15 y is equal to 9 and
here I get 6x plus 12 I is equal to 8
right XS cancel delegate 3y is equal 1
or I will get Y is equal to 1 right I
put Y in any equation I will put little
while put in this equation I will get 3x
plus 6 into y y1 by 3 is equal to 4
right or I will get X is nothing but 4
minus this becomes 2 by 3 right is going
to by
so I have got X is equal to two badly so
I have got the value of x and I got the
value per that means I have got the per
unit per unit work done per day by
minute
correct now the question asked is how
many days are gone women take alone each
over so let's suppose it takes n is n
days into for women the birthday work is
2x3 correct
so any two by three is equal to total
August well behaved as you even if you
don't does if we put W it will solve you
will get answer but just to make our
life simple and M taken film right so
this becomes R and we'll come out to it
value into 3 by 2 that is e team second
key is for men per unit work is 1 by 3
into 1 by 3 is 1 into n or n is equal to
these six so men will take 36 days to
finish the work alone and women they
eighteen days to finish the work alone
very simple what we have done
just try to understand we have assumed
unique work per day done by when we went
to be X admire please note it is unique
work per day to be x and y so they are
two women so 2x per day work done by
women they are five minutes to five by
work per day by min total work per days
2x plus 5 5 total work in four days
because board is it 2 is equal to W
similarly in this case 3x plus 6 person
please Linda Lou I assume double to be
12 just to make my life simpler if I
keep the middle work I tip the blue to
beat well because that divides both 400
so I got two equations very simple
equations and I got X to be 2 by 3 by
doing with my three that means mmmm is
take doing 2 by 3 into work per day and
man is doing 1
but as he noted work is 12 minutes bring
good luck against well units right you
see here other units this is both per
day in units by day this is unit this is
unit everything is in it so you got X is
equal to 1 by 3 units work per day and X
equal to 2 by 3 you need to work part a
and y is equal to 1 by the unit work
part so not this per day so we have
multiplied with n right n into 2 by 3 is
going to be well total of August 1 and
came out to be 18 days in this case NK
movie let's take my example Louie
travels she hundred kilometer to her
home partly by train and partly - she
takes force R if she travels 60
kilometer by train and the meaning my
bus if she travels 100 kilometer white
male and remaining my bus he takes 10
minutes Naga
find the speed of training so let us
suppose this lead is VP the velocity of
plane and this is VB LST of bus to
ordered lesson since 300 kilometer now C
takes for our for this is a time
national right
I mean something but distance by speed
correct C takes for our UC travel 60
kilometer of 1860 by train the remaining
is 300 minus 60 go for the Vipers total
diamonds for ours
you see Traverse hundred kilometer by
train this is hundred kilometer by train
the meaning is 300 - hundred two hundred
members see you take ten minutes long
other dense
4 plus 10 by 60 hours I covered
everything in ours this is what we are
told now time is equal to distance by
speed in first case distance is 16 speed
is V T so 60 by VT
Plus hey this is 240 and speed is V B
this is for equation in the wall second
gaze train distance is 100 100 by VD
plus 200 by V V this is nothing for 10
by 60 that is 4 1 by 6 this comes out to
be 25 by 6 6 into 4 24 plus 125 I since
these are the two equations we have fun
now this is not a linear equation
equation hotter then I say 1 by V T is
good to a and 1 by V B is going to be we
have done this so I'll write this
equation as 16 a plus 240 B is equal to
4 and this equation as 100 a plus 200 V
is equal to 25 by 6 6 I'll multiply here
this becomes 16 200-600 6 into 2 n 1200
these are the two equation we have got
now in this equation if you multiply by
10 a in the common you cancel right so
I'll multiply by 10 so this becomes
we'll multiply this by 10 and stay so
what I will get to lightly late the
final equation here 618 + 2 4 0 0 B is
equal to 40 and here 600 a plus 1200 B
is equal to 25 let's a practice this
cancel my Daquan it minus 21 is again -
100 V is equal to 40 minus 25 is 50
correct so I will get V is equal to 15
by 1200 you solve this this becomes 1 by
8 you put the value of B in this
equation in equation catarrhal ok so
let's go
in this equation 16 a plus 2 14 degree
is 2 4 T by a t is equal to 4 8 into 3
is 24
so what I'll get is nothing but 4 minus
3 is 1 by 16 so I got a is going to 1 by
60 and vs / 2 1 by T this I have now a
is nothing but 1 by V T he resumed is
here you see this is equal to 1 by 16 so
we can see that VT is nothing but 60
kilometer 1 power
similarly V is nothing but 1 by V R that
is nothing but 1 by 80 so we can see
that VR is going to 80 kilometer per
hour right that is all we have got the
velocity of train and we have got the
velocity of bus this is per session so
what we have done here we know the
distance 60 to 40 MV into the speed VPN
VB we use the formula distance by speed
is equal to time we have added about
time to gain for in this case we've
added the journey time of train and bus
to get 25 s 6 we converted this to a
linear equation by put by assuming 120
is equal to a and that by P is equal to
B we got this equation we solved it we
got the value of a and B and then we
know a is equal to 1 by V T that is 1 by
60 so we got B is equal to 60 and V 0 to
1 by V B that is one way it needs to be
visible to a degree
thank you visit exam viacom to watch
free education videos try free online
tests get the best quality study
materials study from the best tutors and
mentors and much more thanks and serene
equations in two variables part 18 is
brought you by exam fear calm no more
fear from exam before watching this
video please make sure that you have
washed videos part 1 - part 17 for
example two men and five two women and
five men can together finish work in
four days three when Hoover and six
pension finishings three days fine time
taken by one man alone and also by one
man let's write whatever is written here
two women and five men they take four
days also three women six men they take
three days we have to find nine taken by
one man to finish the book so let's
assume let's assume that this man does
xqe of work reading X unit of work per
day let's assume this women does exeunt
per day because women was first and men
does why you read buddy right that is
unique per day you need to work per day
this guy is doing X you need work party
this lady and this guy is doing while it
work now since they are taking four and
three days I can assume that total
working stuff
big double total work total over his
winter I can take any value is the best
way to solve this questions is you can
take the W to be LCM of these values and
tell you why because you could take the
LCM of this values it cuts until if I
first see if this guy is the woman is
doing X need of work party and the man
is doing y unit of all party since the
women is taking Ted to women so per day
work done by women is 2x because their
two women
and per day world in my - bye-bye
because there are five men in first case
this forever and they are taking four
days this is total about them you says
nothing but in second case per day work
them maybe minus 3x while because they
are three women per day work done by
minus six why why because they are six
men and the total time taken is three
days this is over I can take W has to be
any well doesn't matter
you simply my my question what I do I am
they W to be LCM of this because
whatever number I take still cut this
will divide by four to every three so
I'd take that would to be twenty thus
for my convenience I can take 24 also
getting any value but if I take twelve
ready for anything that divides both for
entry that this easy for real is because
this will divide and I will get a
simpler equation so I will take it to
individual and here also I take the
equation I get is because this four is
gone now and three is again haircut so I
will get 2x plus 5y is equal to 3 that
is first equation and 3x plus 6y four is
second division now let's solve it so
let me divide multiply this whole thing
by 3 and this by 2 because in this case
both will have 6 accelerate cancel so I
will get 6x plus 15 y is equal to 9 and
here I get 6x plus 12 I is equal to 8
right XS cancel delegate 3y is equal 1
or I will get Y is equal to 1 right I
put Y in any equation I will put little
while put in this equation I will get 3x
plus 6 into y y1 by 3 is equal to 4
right or I will get X is nothing but 4
minus this becomes 2 by 3 right is going
to by
so I have got X is equal to two badly so
I have got the value of x and I got the
value per that means I have got the per
unit per unit work done per day by
minute
correct now the question asked is how
many days are gone women take alone each
over so let's suppose it takes n is n
days into for women the birthday work is
2x3 correct
so any two by three is equal to total
August well behaved as you even if you
don't does if we put W it will solve you
will get answer but just to make our
life simple and M taken film right so
this becomes R and we'll come out to it
value into 3 by 2 that is e team second
key is for men per unit work is 1 by 3
into 1 by 3 is 1 into n or n is equal to
these six so men will take 36 days to
finish the work alone and women they
eighteen days to finish the work alone
very simple what we have done
just try to understand we have assumed
unique work per day done by when we went
to be X admire please note it is unique
work per day to be x and y so they are
two women so 2x per day work done by
women they are five minutes to five by
work per day by min total work per days
2x plus 5 5 total work in four days
because board is it 2 is equal to W
similarly in this case 3x plus 6 person
please Linda Lou I assume double to be
12 just to make my life simpler if I
keep the middle work I tip the blue to
beat well because that divides both 400
so I got two equations very simple
equations and I got X to be 2 by 3 by
doing with my three that means mmmm is
take doing 2 by 3 into work per day and
man is doing 1
but as he noted work is 12 minutes bring
good luck against well units right you
see here other units this is both per
day in units by day this is unit this is
unit everything is in it so you got X is
equal to 1 by 3 units work per day and X
equal to 2 by 3 you need to work part a
and y is equal to 1 by the unit work
part so not this per day so we have
multiplied with n right n into 2 by 3 is
going to be well total of August 1 and
came out to be 18 days in this case NK
movie let's take my example Louie
travels she hundred kilometer to her
home partly by train and partly - she
takes force R if she travels 60
kilometer by train and the meaning my
bus if she travels 100 kilometer white
male and remaining my bus he takes 10
minutes Naga
find the speed of training so let us
suppose this lead is VP the velocity of
plane and this is VB LST of bus to
ordered lesson since 300 kilometer now C
takes for our for this is a time
national right
I mean something but distance by speed
correct C takes for our UC travel 60
kilometer of 1860 by train the remaining
is 300 minus 60 go for the Vipers total
diamonds for ours
you see Traverse hundred kilometer by
train this is hundred kilometer by train
the meaning is 300 - hundred two hundred
members see you take ten minutes long
other dense
4 plus 10 by 60 hours I covered
everything in ours this is what we are
told now time is equal to distance by
speed in first case distance is 16 speed
is V T so 60 by VT
Plus hey this is 240 and speed is V B
this is for equation in the wall second
gaze train distance is 100 100 by VD
plus 200 by V V this is nothing for 10
by 60 that is 4 1 by 6 this comes out to
be 25 by 6 6 into 4 24 plus 125 I since
these are the two equations we have fun
now this is not a linear equation
equation hotter then I say 1 by V T is
good to a and 1 by V B is going to be we
have done this so I'll write this
equation as 16 a plus 240 B is equal to
4 and this equation as 100 a plus 200 V
is equal to 25 by 6 6 I'll multiply here
this becomes 16 200-600 6 into 2 n 1200
these are the two equation we have got
now in this equation if you multiply by
10 a in the common you cancel right so
I'll multiply by 10 so this becomes
we'll multiply this by 10 and stay so
what I will get to lightly late the
final equation here 618 + 2 4 0 0 B is
equal to 40 and here 600 a plus 1200 B
is equal to 25 let's a practice this
cancel my Daquan it minus 21 is again -
100 V is equal to 40 minus 25 is 50
correct so I will get V is equal to 15
by 1200 you solve this this becomes 1 by
8 you put the value of B in this
equation in equation catarrhal ok so
let's go
in this equation 16 a plus 2 14 degree
is 2 4 T by a t is equal to 4 8 into 3
is 24
so what I'll get is nothing but 4 minus
3 is 1 by 16 so I got a is going to 1 by
60 and vs / 2 1 by T this I have now a
is nothing but 1 by V T he resumed is
here you see this is equal to 1 by 16 so
we can see that VT is nothing but 60
kilometer 1 power
similarly V is nothing but 1 by V R that
is nothing but 1 by 80 so we can see
that VR is going to 80 kilometer per
hour right that is all we have got the
velocity of train and we have got the
velocity of bus this is per session so
what we have done here we know the
distance 60 to 40 MV into the speed VPN
VB we use the formula distance by speed
is equal to time we have added about
time to gain for in this case we've
added the journey time of train and bus
to get 25 s 6 we converted this to a
linear equation by put by assuming 120
is equal to a and that by P is equal to
B we got this equation we solved it we
got the value of a and B and then we
know a is equal to 1 by V T that is 1 by
60 so we got B is equal to 60 and V 0 to
1 by V B that is one way it needs to be
visible to a degree
thank you visit exam viacom to watch
free education videos try free online
tests get the best quality study
materials study from the best tutors and
mentors and much more thanks and serene
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Nov 15, 2024 Last updated |
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