Today our topic of discussion is Simple Simultaneous Equations in Two Variables Exercises 12.4.
Simple Simultaneous Equations in Two Variables Exercises 12.4
Exercise 12.4
1. For which of the following conditions is the system of equations ax by + c = 0 and px + qy + r = 0 consistent and mutually independent?
1) a/p ne b q
2) a/p = b/q = c/r
3) a/p = b q ne c r
4) a/p = b/q
2. If x + y = 4 x – y = 2 which one of the following is the value of (x, y)?
1) (2,4)
2) (4,2)
3) (3,1)
4) (1,3)
3. If x + y = 6 and 2x = 4 what is the value of y?
1) 2
2) 4
3) 6
4) 8
4. For which one of the following equation is the adjoining chart correct?
1) y = x – 4
2) y = 8 –
3)y = 4 – 2x
4) y = 2x – 4
5. If 2x – y = 8 and x – 2y = 4 then x+y=what?
1) 0
2) 4
3) 8
4) 12
- The equations x – y – 4 = 0 and 3x – 3y – 10 =0:
(i) are mutually dependent.
(ii) are mutually consistent..
(iii) do not have any solution.
On the basis of information above, which one of the following is correct?
1) i
2) iii
3) i and iii
4) ii and iii
On the basis of information given below answer questions 7-9.
Length of the floor of a rectangular room is 2 metres more than its breadth and perimeter of the floor is 20 metre. For decorating the floor with mosaic it costs Tk. 900 per square metre.
- What is the length of the floor of the room in metre?
1) 10
2) 8
3) 6
4) 4
- What is the area of the floor of the room in square metre?
1) 24
2) 32
3) 48
4) 80
- How much taka will be the total cost for decorating the floor with mosaic?
1) 72000
2) 43200
3) 28800
4) 21600
Solve by forming simultaneous equations (10-17):
- If 1 is added to each of numerator and denominator of a fraction, the fraction 4 will be. Again, if 5 is subtracted from each of numerator and denominator, the fraction will be Find the fraction. 2
- If 1 is subtracted from numerator and 2 is added to denominator of a fraction, 1 the fraction will be. Again, if 7 is subtracted from numerator and 2 is 1 subtracted from denominator, the fraction will be Find the fraction. 3
- The digit of the units place of a number consisting of two digits is 1 more than three times the digit of tens place. But if the places of the digits are interchanged, the number thus found will be equal to eight times the sum of the digits. What is the number?
- Difference of the digits of a number consisting of two digits is 4. If the places of the digits are interchanged, sum of the numbers so found and the original number will be 110; find the number.
- Present age of mother is four times the sum of the ages of her two daughters. After 5 years, mother’s age will be twice the sum of the ages of the two daughters. What is the present age of the mother?
- If the length of a rectangular region is decreased by 5 metre and breadth is increased by 3 metre, the area will be less by 9 square metre. Again, if the length is increased by 3 metre and breadth is increased by 2 metre, the area will be increased by 67 square metre. Find the length and breadth of the rectangle.
- A boat, rowing in favour of current, goes 15 km per hour and rowing against the current goes 5 km per hour. Find the speed of the boat and current.
- A labourer of a garments serves on the basis of monthly salary. At the end of every year she gets a fixed increment. Her monthly salary becomes Tk. 4500 after 4 years and Tk. 5000 after 8 years. Find the salary at the beginning of her service and amount of annual increment of salary.
18. A system of simple equations is x + y = 10 3x – 2y = 0
1) Show that the equations are consistent. How many solutions do they have?
2) Solving the system of equations, find (x, y) .
3) Find the area of the triangle formed by the straight lines indicated by the equations with the X-axis.
- If 7 is added to the numerator of a fraction, the value of the fraction is the integer 2. Again, if 2 is subtracted from the denominator, value of the fraction is the integer 1.
1) Form a system of equations by the fraction x/y
2) Find (,y) by solving the system of equations by the method of cross- multiplication. What is the fraction?
3) Draw the graph of the system of equations and verify the correctness of the obtained values of (x, y).
- If the total number of sides of two polygons is 17 and total number of diagonals of those polygons is 53, then what is the number of sides of each polygon?
- An assignment was given to some students where they can work alone or in a male-female group of two members. 2/3 of male students and 3/5 of female students worked in groups. What fraction of students did that assignment alone?
- It takes 5 seconds for two trains of 100 and 200 metre lengths to cross each other when they pass in the opposite direction and 15 seconds in the same direction. Find the velocity of the two trains.
- How many con ecutive integers are needed so that their product is divisible by 5040?
- How many times the hour hand and minute hand of a clock make an angle of 30 degree with each other? Find the times.
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