Solved Question and Answers: Linear Equations | Mathematics (Maths) Class 9 PDF Download

Q1: The positive solution of equation ax + by + c = 0 always lie in the:
(a) 3^rd quadrant
(b)  I^st quadrant
(c) 4^th quadrant
(d) 2^nd quadrant
Ans: b
Sol: The solution of the linear equation is represented by the ordered pair (x,y)
Hence if x>0 , y>0 , then the solution will always lie in the first quadrant.

Q2: For two lines 2x + y = 1 and x – y = 2 if the x coordinate of the common point is 1 what is the y coordinate?
(a) -1
(b) 2
(c) -2
(d) 3
Ans: a

Q3: Which of the following points lies on the line 3x + 2y = 6?
(a) (1, 2)
(b) (3, 0)
(c) (2, 3)
(d) (0, 3)
Ans: d
Sol: Put the given points in the equation 3x + 2y = 6
If L.H.S of the equation is equal to R.H.S
then the given points will lie on the line
3x + 2y = 6
3.0 + 2.3 = 6
6 =6
L.H.S = R.H.S
So the given point lie on the line. 

Q4: Rozly can row downstream 20km in 2 hours, and the upstream 4km in 2 hours. What will be the speed of rowing in still water?     
(a) 4km/hr      
(b) 6km/hr        
(c) 3km/hr      
(d) 7km/hr
Ans: b
Sol: Upstream = (x-y) km/hr
Downstream =(x+y)km/hr
20(x+y)=2
X+Y=10.....(1)
4(x-y)=2
x-y=2....(2)
Solve both equations
x+y=10
x-y=2
2x=12
X=6
Substitute x=6in i
6+y=10
Y=4
Speed of rowing in still water is 6km/hr.
the speed of still water is 4km/hr
So option B is correct answer. 

Q5: The linear equation 2x + 5y = 8 has:
(a) A unique solution
(b) Infinitely many solution
(c) No solution
(d) Two solution
Ans: b

Q6: The value of m, if a = 3 and b = 1 is the solution of equation 2a + 3b = m is:
(a) 9
(b) 10
(c) 8
(d) 7
Ans: a
Sol: In the given question we have  a=3,b=1 the given equation is 2a + 3b=m
By substituting the values of a,b in the given  equation, we get ,
 2 x 3 + 3 x 1 = m
6 + 3 = m
9 = m
So option A is the correct answer. 

Q7: Which of the following is the solution of linear equation
(a) (1, -5)
(b) (-1, -5)
(c) (-1, 5)
(d) (1,5)
Ans: c

Q8: All linear equations in two variables have ————– .
(a) One solution
(b) Infinitely many solutions
(c) Three solutions
(d) Two solution
Ans: b

Q9: The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is:
(a) 6
(b) 5
(c) 7
(d) -7
Ans: c
Sol: If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then these values will satisfy the equation. So, putting x = 2 and y = 1 in the equation, we get
2(2) + 3(1) = k
⇒ 4 + 3 = k
⇒ k = 7.

Q10: If -0.25x + 1.3 = -0.55x – 0.2, then x
(a) -2
(b) -5
(c) 5
(d) 2
Ans: b
Sol: Given equation is :
-0.25x + 1.3 = -0.55x – 0.2
-0.25x + 0.55x = -0.2 - 1.3
0.30 x = -1.5
So x = -1.5 / 0.30
x = -5
So option B is correct answer. 

Q11: The point lying on the equation 2x – y = 5 is:
(a) (3, 4)
(b) (-3, 1)
(c) (6, 1)
(d) (2, -1)
Ans: d
Sol: The point will lie on the line if L.H.S of the equation is equal to R.H.S
Given equation is 2x - y = 5
Put the point ( 2 , -1) in the above equation
2 . 2 - (-1) = 4 + 1 = 5 = R.H.S
So this proves that the given points lie on the line.
So option D is correct answer.  

Q12: The value of k if x = 2, y = 1 is a solution of equation 2x – k = – 3y is
(a) 7
(b) -7
(c) 6
(d) 5
Ans: a
Sol: 2*2-k=-3*1(by putting the value of X and y)
4-k=-3
4+3=k
k=7

Q13: Point P(2,-3) lies on the line represented by the equation:
(a) x + 2y = 0
(b) x + y = 1
(c) 2x + y = 1
(d) 2x + 2y = 0
Ans: c

Q14: Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and 3a – 2b = 1
(a)a = 2, b = 3
(b) a = 1, b = 2
(c) a = 1, b = 1
(d) a = 4, b = 1
Ans: c
Sol: Given Equations
ax + by = 3    {1}
3a - 2b = 1     {2}
x = 2, y = 1 ( given)
Equation {1} becomes,
2a + b = 3      {3}
Substract equation {3} from {2}, we get,
2a + b - 3a + 2b = 3 - 1
-a + 3b  = 2
3b = 2 + a
b = (2+a) / 3
Put the value of b in equation {3}, we get
2a + (2 +a ) / 3 = 3
(6a +a +2) / 3 = 3
7a + 2 = 9
a = 1
Now put value of a in {3}
2 + b = 3
b = 1
hence we get value of a and b i.e. 1 and 1 

Q15: Which of the following is a solution of the equation 4x + 3y = 16?
(a) (1, 3)
(b) (2, 3)
(c) (2, 4)
(d) (1, 4)
Ans: d
Sol: Given equation is :
4x + 3y = 16
Putting x = 1 and y = 4
4 .1 + 3. 4 = 16
4 + 12 = 16
16 = 16
So option D is the correct answer.

Q16: Solutions of the equation 2x + 5y = 0 is:
(a) 3,0
(b) -3,2
(c) 0,0
(d) 0,4
Ans: c

Q17: (2,-3) is a solution of 3x + 4y + k = 0. So, the value of k must be
(a) -6
(b) 6
(c) -4
(d) 4
Ans: b

Q18: If the line represented by the equation 3x + αy = 8 passes through the points (2,2), then the value of α is
(a) 0
(b) 4
(c) 3
(d) 1
Ans: d
Sol: Given that the equation 3x + ay = 8 passes through the point (2,2) it means that (2,2) is a solution of the equation
Putting X= 2 and Y = 2 in the equation we have  
3(2) + a (2) = 8
6 + 2a = 8
2a = 8-6
2a = 2
a = 2/2 = 1
Therefore value of
a = 1
So option D is correct answer. 

Q19: The number of lines passing through (3, 4) are
(a) 1
(b) 2
(c) 0
(d) Infinite
Ans: d