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Class 10 Maths Problems for Linear equation



Given below are the Class 10 Maths Problems for Linear equation
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blank's
1) In a cyclic quadrilateral ABCD, Find the four angles.
a) <A = (2x + 4), <B = (y + 3), <C = (2y + 10), <D = (4x -5).
b) <A = (2x – 1), <B = (y + 5), <C = (2y + 15) and <D = (4x -7).  c)  <A = (2x – 1), <B = (y + 5) ,<C = (2y + 15) and <D = (4x – 7).
d)  <A = (2x + 4), <B = (y + 3), <C = (2y + 10), <D = (4x – 5).
2) Given below are three equations. Two of them have infinite solutions and two have a unique solution. State the two pairs:
3x – 2y = 4
6x + 2y = 4
9x -6y = 12.
3) Find the values of a and b for which the following system of linear equations has infinite number of solutions:
2x + 3y = 7; 2ax + (a + b)y = 28.
4) Find the values of a and b for which the following system of linear equations has infinite number of solutions:
2x -3y = 7; (a + b)x – (a + b- 3)y = 4a + b.
5) In a ABC, <A = x, <B = (3x -2), <C = y. Also <C - <B = 9. Find the three angles.
6) Find the value of k for which the system of equations x + 2y – 3 = 0 and ky + 5x + 7 = 0 has a unique solution.
7) For what value (s) of ‘a’, the system of linear equations 2x + 3y = 7 and (a – 1)x + (a + 1)y = 3a + 1 represent parallel lines.
8) If the lines x + 2y + 7 = 0 and 2x + ky + 18 = 0 intersect at a point, then find the value of k.
9) Is x = 5, y = -5 a solution of the linear equation 3x + 2y – 5 = 0?
10) The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. Find the present ages of the son and the father.
11) Replace ‘p’ by an appropriate number so that the following system of equations has a unique solution.
2x + 3y = 5
px +9y = 12
12) For what value of k, the following pair of linear equations has infinitely many solutions?
i) kx + 4y – (k + 8) = 0
        4x + ky + 4 = 0
ii) 2x + 3y = 4
(k + 2)x + 6y = 3k + 2
13) For what value of k, will the following system of equations have no solutions?
i) (3k + 1) x + 3y = 2; (k2 + 1) x + (k – 2) y = 5
ii)
3x + y = 1
(2k – 1) x + (k – 1) y = 2k + 1
iii)
2x + ky = 11
5x – 7y = 5
14) For what value of k, does the pair of equations given below has a unique solution?
2x + ky = 6, 4x + 6y = 0
15) Find the value of k for which the following system of linear equations has infinite solutions:
i) x + (k + 1) y = 5
(k + 1) x + 9y = 8k – 1
ii)
8x + 5y = 9
kx + 10y = 18
iii) 2x + 3y = k
(k – 1) x + (k + 2) y = 3k
16) For what value of α, the system of equations
αx + 3y = α – 3
12x + αy = α
will have no solution?
17) Find the value of k for which the system
kx + 2y = 5
3x + y = 1
has (i) a unique solution, and (ii) no solution.
18) Find the value of k for which the system
2x + ky = 1
3x – 5y = 7
has (i) a unique solution, and (ii) no solution.
19 )find the value of a and b for which the following system of equations has infinitely many solutions:
2x – (2a + 5) y = 5
(2b + 1) x – 9y = 15
20) Find the value of a for which the following system of equations has infinitely many solutions:
2x + 3y – 7 = 0
(a – 1) x + (a + 1) y = (3a – 1)
Answer
1)
ii) 65, 55, 115, 125
iii) 65, 55, 115, 125.
iv) 10, 53, 110, 127
2) 1 & 3, 1 & 2
3) 4,8
4) -5,-1
5) 25,73, 82
6) k  10
7) 5
8) k  4
9) Yes
16) -6
17) k≠6 , k=6
18) k≠ -10/3  , k=10/3
19) (-1, 5/2)
20) a=5  

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