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If the point P(x,y) is equidistant from the points A(a-b, a+b) and B(a+b, b-a) then prove bx=ay.
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Q.1=DRAW THE GRAPH OF x+y+1=0 and 3x +2y-12=0.Determine the coordinates of the vertices of the triangle formed by these lines and x axis .Calculate the area bounded by these lines and x axis.
check graphically whether the pair of equations 3x - 2y + 2 = 0 , 3/2x - y + 3 = 0 is consistent. Also find the co-ordinatesof the point , where the graph of the equations meet the y axis
how to solve (a-b)x + (a+b)y = (a2-2ab-b2) , (a+b) (x+y)=a2+b2. by cross multiplication method
The equations ax + by +c = 0 and dx + ey + c =0 represent the same straight line if
a. ad = be b. ac = bd c. bc = ad d. ab = de
a plane left 30 minutes later than the scheduled time and inorder to reach the desination, 1500km away in time. It has to increase the speed by 250km/h from the usual seed. Find the usual speed?
The area of the triangle formed by the lines x =3,y = 4 and x = y is:
1) 1/2 sq. unit 2) 1 sq. unit 3)2 sq. units 4) none of these
answer:- option 1).
solve for x and y
x / a + y / b = 2 ; ax - by = a2 - b2
A boat goes 30 Km upstream and 44 KM downstream in 10 hours.In 13 hours, it can go 40 KM upstream and 55 KM down- stream. Determine the speed and that pf the boat in still water....????
kindly explain this question....
How many solutions does the pair of equations x + 2y = 3 and 1/2x +y -3/2 = 0 have?
2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish in 3 days. find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone
Solve the following pair of equations
2/root x + 3/root y =2 and 4/root x - 9/root y = -1
A man travels 600km partly by train and partly by car. If he covers 400km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and rest by car, he takes half an hour longer. Fine the speed of the train and that of the car
The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if
a. a=b b. 3a = 2b c. 2a = 3b d. ab = 6
Students of a class are made to stand in rows. If one student is extra in a row, there would be 2 rows
three lines x+3y=6 ,2x-3y=12 and x=0 are enclosing a beautiful triangular park.find the points of intersection of the lines graphically and the area of the park if all the measurements are in km.
Points A and B are 90 km apart from each other on a highway. A car starts from A and another from B at the same time. If they go in the same direction they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. Find their sppeds.
What is the meaning of non-zero solution. For what value of p does the system of equation 2x-py=0, 3x+4y=0 has non zero solution
Places A and B are 100 km apart on a highway. One car starts from A and another
for what value of K will the following pair of linear equation have no solution
find relation between p and q if x=3,y=1 is asolution of a pair of lines x-4y+p=0 and 2x+y-q-2=0
covered a certain distance at a uniform speed. If the train would
have been 10 km/h faster, it would have taken 2 hours less than the
scheduled time. And if the train were slower by 10 km/h; it would
have taken 3 hours more than the scheduled time. Find the distance
covered by the train.
A train covered a certain distance at a uniform speed. If the train would have been 6km/hr. faster, it would have taken 4 hours less than the scheduled time. And if the train were slower by 6km/hr. it would have taken 6 hours more than the scheduled time. Find the length of the journey.
A sailor goes 8 km downstream in 40 minutes and returns in 1 hour.Determine the speed of the sailor in still water and the speed of the current?
Two lines are given to be parallel. The equation of one of the lines is 4x + 3y = 14. Find the equation of the second line.
A two digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting by 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.
. Solve for x and y : 23x + 35y = 209 35x + 23y = 197
1/2(2x+3y)+12/7(3x-2y)=1/2 & 7/2x+3y +4/3x-2y=2.sove the following equations
seven times a two digit number is equal to four times the number obtained by reversing the order of its digits if the difference between the digits is 3 , find the number
If students of a class are made to stand in rows,if 3 students are extra in a row ,there would be 1 row less .if 3 student are less in a row there would be 2 rows more .find the number of students in the class .please form the equation and solve it with proper explaination.
Half the perimeter of a rectangular garden, whose length is 4m more than its width,is 36m. Find the dimensions of the garden.
3. When lines l1 and l2 are parallel, then the graphical solution system of linear equation have
(a) infinite number of solutions (b) unique solution
(c) no solution (d) one solution
the sum of the numerator and denominator of a fraction is 3 less than twice the denominator. if the numerator and denominator are decreased by 1,the numerator becomes half the denomiator.find the fraction.
8 men and 12 boys can finish a piece of work in 10 days while 6 men and boys can finish it in 14 days find the time taken by one man alone and that by one boy alone to finish the work
1. Find graphically the coordinates of the vertices of a triangle whose sides have the equations:
(i) y = x, y = 0 and 2x + 3y = 30
(ii) y = x, 3y = x and x + y = 8
(iii) 2y –x = 8, 5y – x = 14 and y – 2x = 1
The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
Can you do this question by Elimination Method??
A person, rowing at the rate of 5 km/hr in still water, takes thrice as much time in going 40 km upstream as in going downstream. Find the speed of the stream.
Pls tell how to solve this
A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21km downtream in 6.5 hours. Find the speed of the boat in the still water and the speed of stream.
4 men and 6 boys can finish a piece of work in 5 days while 3 men and 4 boys can finish it in
Solve x and y: x+6/y=6, 3x-8/y=5.
On selling a tea-set at 5% loss and a lemon-set at 15% gain, a crockery seller gains Rs. 7. If he sells
the pair of linear equation x=y and x+y=0 has
tick the correct answer
a.no common solution
b.infinitely many solutions
c. unique solution
It takes 12 hours to fill a swimming pool using 2 pipes. If a pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half the pool can be filled. How long it would take for each pipe to fill the pool separately? Give answer ASAP
mx-ny=m2 + n2 ; x+y = 2m
x takes 3 hours more than y to walk 30 km. but if x doubles his pace, he is ahead of y by one and a half hours. find their speeds of walking.
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream.Ddetermine the speed of the stream and that of boat in water.
The pair of linear equations 3x + 4y = 12 and y =4 has
a. no common solution b. infinetly many solutions c. unique solution d. none of these
Solve by cross -multiplication method : x+y = a+b, ax-by = a2-b2
A girl walks 200 towards East and the she walks 150m towards North. The distance of the girl
from the starting point is
(a) 350m (b) 250m (c) 300m (d) 225m
The pair of linear equations 2x +3y = 5 and 4x + 6y = 10 is
a. inconsistent b. consistent c. dependent consistent d. none of these
The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. FInd the number.
how do i find it ??
'A' takes 3 hours more than 'B' to walk a distance of 30km. But, if 'A' doubles his pace he is ahead of 'B' by 1.5 hrs. Find the speed of 'A' and 'B'?
if √ax-√by=b-a and √bx-√ay=0 then value of x,y is
solve the following simultaneous equations:
(i) 3/rootx+4/rooty=17/6 ; 5/rootx-6/rooty=1/2
(ii) 2(3x-y)=5xy ; 2(x=3y)=5xy (x is not equal to 0,y is not equal to 0)
Solve (a-b)x + (a+b)y = asquare - 2ab - b square and (a+b)(x+y) = a square +b square.
draw the graph of the equation
y=2x-2 and y=4x-4 and find the area of the triangle bounded by these lines and axis by y.
after covering a distance of 30 km with a uniform speed there is some defect in a train engine and therefore; its speed is reduced to 45 of its orignal speed.consequently, the train reaches is destination late by 45 minutes.Had it happened after covering 18 kilometers more, the train would have reached 9 minutes earlier.Find the speed of the train and the distance of the journey. HURRRRY HURRRY GIVE THE ANSWER
If cosec (A+B) =1 and sec(A-B)=2, evaluate:
i). Sin A cos B + cos A sinB
ii). tan A + tan B
1-tanA * tanB
For what values of a and b does the following pair of linear equations has a infinite number of solutions: 2x+3y=7; a(x+y)-b(x-y)=3a+b-2.
a boat covers 32km upstream and 36km downstream in 7hours. also it covers 40km upstream and 48km downstream in 9hours. find the speed of the boat in still water and that of stream?
How many solutions does the pair of equations y=0 and y = -x has? explain
A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs. 1000 as hostel charges whereas a student B,who takes food for 26 days,pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
b/a x + a/b y = a2 + b2 , x+y =2ab solve for x and y
RD Sharma solution
For a pair to be consistent and dependent the pair must have
A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour
A wizard having the powers of mystic in candations and magical medicines seeing a cock fight going on, spoke privately to both the owners of the cocks. To one he said; if ur bird wins then you give me your stake money but if you don't win i shall give you two third of that.Going to the other he promised in the same way to give 3/4th . from both of them his gain could only be 12 gold coins. find the stake of money of each of the cock-owners have.
Two numbers are in the ratio 5:6. If 8 is subtracted from each of the numbers, theratio becomes 4:5. Find the numbers.
the sum of numerator and denominator of fraction is 4 more than twice the numerator.
if the numerator and denominator are increase by 3 they are in the ratio 2:3.find the fraction
Given the pair of equations ax + (a - 1) y = 1 and (a + 1) x - ay = 1, for which one of the following values of a is there no common solution of the given pair of equations?
a + - root 2 b. +- 1 / root 2 c. + - 2 d. 1 + - 1 / 2
Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
solve by elimination method :
2power x + 3 power y=17
2 power (x+2) + 3 power (y+1)=5
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