## Thursday, July 12, 2012

### Pair of Linear Equations

Practice Questions
1. Check whether :
a) x=5 and y = -2 is a solution of the system of simultaneous linear equations 2x+3y=4 and 3x+5y=5
b) x=-2 and y = -1 is a solution of the system of equations 3x+y+2=0 and 3x+y-5=0 State, in each case, whether system is consistent or inconsistent.
2. Solve , graphically , each of the following system of equations : a) 2x-3y=2 , x+2y=8 b) x+y=3 , 3x-2y+7=0 c) 2x+3y=8 , 4x+1.5y=7
3. Draw the graph of : 6x+5y=37 , 4x+7y=21 and x-y+3=0. From the graph read the vertices of triangle obtained.
4. Show , graphically , that the following system of equations has an infinite number of solutions : 2y=4x-6 and 2x=y+3
5. Solve the following system of linear equations graphically : x-y=1 and x+2y=7. Shade the area bounded by lines and the y-axis.
6. By drawing graph of each of the equations : 3x+y+5=0 , 3y-x=5 and 2x+5y=1 on the same graph paper , show that the lines given by these equations , are concurrent i.e. they pass through the same point.
7. Draw the graph of the equations: 6y=5x+10 and y=5x-15. From the graph , find : a) the coordinates of the point , where the two lines intersect. b) the area of the triangle between lines and the x- axis.
8. Use the method of elimination by substitution to solve each of the following system of linear equations : a) 5x-3y=1 , x-2y=3 b) 2x+y=3 , 3x-2y=8 c) x/3 + y/4 = 6 ,   x/6 + y/2 = 6 d) 1/x+1/y=2 , 1/y-1/x=6
9. Solve the following system of linear equations using the method of elimination by equating the coefficients: a) 5x+2y=2 , 2x+3y=-8 b) 2x-3y=7 , 4x+5y=3
10.  Using the method of cross – multiplication ; solve each of the following system of linear equations :a) 3x+2y=12 , x+4y=9 b) ax+by=a-b , bx-ay=a+b
11.  Solve : a) 2x+y=2xy , 8x+3y=15xy b) 2(7x+4y) = xy , 2(3x+2y) = 3xy
12. Solve : a) 103x+51y=617 , 97x+49y=583 b) 15x-14y = 117 , 14x – 15y = 115
13. A railway half ticket costs half of the full fare and the reservation charges are the same on half ticket as on full ticket. One reserved 3 A.C. class ticket from New Delhi to Lucknow costs Rs.538 and one half reserved 3 A.C. class ticket costs Rs.294. Find the full basic fare and the reservation charges separately.
14. A boat goes 30 km upstream and 44 km downstream in 10 hours. It can go 40 km upstream and 55 km downstream in 13 hours. Find the speed of the stream and that of the boat in still water.
15. A person travels 600 km to his home, partly by train and partly by car. He takes 8 hours if he travels 120 km by train and the rest by car. He takes 20 minutes longer if he travels 200 km by train and the rest by car. Find the speeds of the train and the car.
16. The ten’s digit of a number is twice the unit’s digit. The number obtained on interchanging the digits is 36 less than the original number. Find the original number.
17. One added to eight times the sum of its two digits gives us that number. This number is also obtained by adding 2 to 13 times the difference of its digits. Find the number. How many such numbers are there?
18. A father’s age is thrice the sum of the ages of his two children. After five years , his age will be twice the sum of their ages. How old is the father?
19. In a triangle ABC , ∠A=xº , ∠B=3xº and ∠C = yº. If 3y-5x=30º. Prove that the triangle is a right-angled triangle.
20. A number consists of two digits. When it is divided by the sum of the digits , the quotient is 7. The sum of the reciprocals of the digits is 9 times the product of the reciprocals of the digits. Find the numbers.