These Mathematics Questions of Chapter {Pair of Linear Equation of two variables} are important for CBSE Examination 2023. So all the candidates Revise and Practices all the questions carefully
1)
Determine
the value of k for which the given system of equations has unique solution:
a.
a)
2x – 3y = 1 ; k x + 5y = 7
b) 4x – 5y = k ; 2x – 3 y = 12
2)
Find the value of k, for which the system of
equations has infinitely many solutions.
a)
2x –3y = 7 ; (k+2) x – (2k+1) y = 3(2k–1)
b)
x + (k+1) y =5 ; (k+1) x + 9 y = 8k – 1
3)
Find the value of ‘k’ so that the following
equations has no solution.
a.
(3k+1)
x +3y – 2 = 0 c) (k²+1) x +
(k – 2) y –5 = 0
b.
3x
+ y = 1, (2k – 1)x + (k – 1)y = 2k +
1
4)
Solve
the following equations by method of cross multiplication and elimination
method:
a.
1)
x + 2y + 1=0, 2x –3 y = 12 d) (2u+v) =7uv, 3(u+3v) = 11uv
b.
3)
2x+y – 3=0, 2x – 3y –7= 0 e) x + y = a + b, ax – by = a² – b²
c.
(a
+ 2b)x + (2a – b)y = 2, (a – 2b)x + (2a + b)y = 3 f) 2x = 5y + 4, 3x
– 2y + 16 = 0
5)
Solve the following equations by graphically
and substitution method.
a.
x + y = 3, 2x + 5y = 12 d) x – 2y – 5 =
0, 3x – 6y = 15
b.
2x – 3y +13=0, 3x – 2y + 12 = 0 e) 3x – 4y –1=0, 2x – y + 5 =
0
c.
4x
– y = 4, 3x + 2y = 14
6)
Represent
the following equations on the graph and determine the vertices of the
triangle, so formed. a) 2y – x = 8,
5y – x = 14, y – 2 x = 1 b)
y = x, y = 0, 3x + 3y = 10
7)
Draw the graph of x – y + 1 = 0 and 3x + 2y
–12 = 0. Calculate the area of the triangle bounded by these lines and the
x-axis.
8)
Solve
the system of equations x – y = 1, 2x + y = 8 graphically .Shade the area bounded
by these lines and x-axis. Also find its area.
9)
A
man has belts and handkerchiefs which are together 40 in number. If he had 5
more handkerchiefs and 5 less belts, the number of handkerchiefs becomes four
times the number of belts. Find the
original number of each.
10) The age of father is twice the sum of
ages of his two children. Ten years hence, the age of father will be
three-quarter of the sum of the ages of his children then. Find the present age
of father.
11) The numerator of a fraction is 4 less
than its denominator. If the numerator is decreased by 2 and the denominator is
increased by 1, the denominator becomes 8 times its numerator. Find the
fraction.
12) Solve for x and y : x + 4y = 27xy, x + 2y = 21xy
13) Aditya is walking along the line
joining points (1, 4) and (0, 6). Aditi is walking along the line joining
points (3, 4) and (1, 0). Represent on
graph and find the point where both of them cross each other.
14) For what value of a and b will the
following system of linear equation has infinitely many solutions? 2x – 3y = 7, (a + b)x – (a + b – 3)y = 4a + b
17) The area of rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 sq. units. Find the length and the breadth of the rectangle.
18) Find the value of α and β for which
the following pair of linear equations has infinite number of solutions : 2x +
3y = 7, 2αx + (α + β)y = 28
19) Solve the following system of linear
equations by cross multiplication method :
2(ax
– by) + (a + 4b) = 0, 2 (bx + ay) +
(b – 4a) = 0
20) For which values of a and b does the following pair of linear equations have infinite number of solutions?
2x
+ 3y = 7, (a – b)x + (a + b) y = 3a +
b – 2
21) A chemist has one solution which is
50% acid and a second which is 25% acid. How much of each should be mixed to
make 10 liter of 40% acid solution..jpeg)
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22) 2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?
23) Form a pair of linear equations in two variables using the following information and solve it graphically. Five years ago, Sagar was twice as old as tiru. Ten years later. Sagar’s age will be ten years more the Tiru’s age. Find their present ages.
24) Solve the following pair of linear equations graphically: 2x+ 3y = 12 and x – y = 1 Find the area of the region bounded by the two lines representing the equations and y axis.
25) Amit bought 2 pencils and 3 chocolates for Rs. 11 and Sumit bought 1 pencil and two chocolates of Rs. 7. Represent this situations in the form of a pair of linear equations. Find the price of one pencil and that of one chocolate graphically.
26) A part of a monthly hostel charge is fixed and the remaining depend on the number of days one has taken food in the mess. When Swati take food for 20 days she had to pay Rs. 3000 as hostel charges whereas Mansi who takes food for 25 days Rs 3500 as hostel charges. Find the fixed charges and the cost of food per day.
27) A fraction becomes 9/11 if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator it becomes 5/6. Find the fraction.
28) If 2 is subtracted from the numerator and 1 is added to the denominator, a fraction becomes ½, but when 4 is added to the numerator and 3 is subtracted from the denominator, it becomes 3/2. Find the fraction.
29) A boat covers 32 km upstream and 36 km downstream in 7 hours. Also it covers 40 km upstream and 48 km downstream in 9 hours. Find the sped of the boat in still water and that of the stream.
30) Raghav scored 70 marks in a test, getting 4 marks for each right answer and losing 1 mark for each wrong answer. Had 5 marks been awarded for each correct answer and 2 marks been deducted for each wrong answer, than Raghav would have scored 80 marks. How many questions were there in the test?
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