Are you looking for Linear Equations in Two Variables Extra Questions and Answers, if yes? then you the right place. Here we are providing Linear Equations in Two Variables Extra Questions and Answers Class 9 Maths Chapter 4.
Linear Equations in Two Variables Extra Questions and Answers Maths Chapter 4
- 1 mark mcq
1) Define the graph of linear equation.
Ans=> A linear equation in two variables is represented geometrically by a line whose points make up the collection of solutions of the equation. This is called the graph of the linear equation.
2) The reason that a, degree one, polynomial equation ax + by + c = 0 is called a … .. ..
a) linear equation
b) Geometrical equation
c) Simple equation
d) None of these
Ans-a
3) the graph of every linear equation in two variables is a straight line.
a) true
b) false
Ans=> true
4) y= mx is represented as… .. .
a) a line passing through the origin
b) a line passing through the x-axis
c) a line passing through the y axis
d) a line passing through the both axis.
Ans=> a
5) The graph of the equation 3x + 5y = 8 cuts the x-axis at the point
a) (0, 5)
b) (3, 0)
c) (5, 0)
d) (0, 0)
Ans=> c
6) If (6, 4) is the solution 4x – ky = 8,then k equals of the equation is
a) 2
b) 4
c) 3
d) 0
Ans=> b
7) x+y=0 is the equation of
a) line passing through x-axis
b) line passing through y-axis
c) line passing through origin
d) line passing through single point.
Ans-c
8) The 1st quadrant equation is… .
a) ax + by + c = 0
b) ax – by + c = 0
c) ax + by – c = 0
d) ax-by-c = 0
Ans-a
9) if y = 8 , then write the two variable equation.
a) 1x+1y=8
b) x+y =8
c) x + 1y = 8
d) xy=8
Ans=c
10) A linear equation in one variables has infinitely many solution.
a) True
b) false
Ans-b
11) In equation, 8x +3y-9=0, write the a, b & c form.
a) a=8, b=3, c= -9
b) a=-8, b=3, c=0
c) a=-8, b=-3, c=9
d) a=-8, b=-3, c=0
Ans-a
12) less than 90 degree angle is
a) rectangle
b) right angle
c) acute angle
d) triangle
Ans-c
13) x = 0 is the equation of the y-axis and y = 0 is the equation of the x axis.
a) true
b) false
Ans- a
14) An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and B are not both zero, is called a … . … .
a) linear in one variables.
b) linear in two variables.
c) linear in three variables.
d) linear in quadrent variables.
Ans-b
15) The graph of every linear equation in two variables is a straight line.
a) true
b) false.
Ans-a
16) a linear equation, the geometrical representation is a ……..line.
a) dotted line
b) straight line
c) curve
d) none of these
Ans-b
17) a linear equation in two variables has infinitely many solutions.
a) false
b) true
Ans-a
18) Give the example of infinitly many solutions.
Ans=>
4x-15y=10
Y=(4x-10)/15
Now for infinite values of x, y will also have infinite solutions.
19) Find the value of k, if x = 2, y = 4 is a solution of the equation 3x + 5y = k.
a) 25
b) 26
c) 27
d) 28
Ans-b
20) The coordinate axes namely x-axis and y-axis can be represented as y=0 and x=0, respectively.
a) true
b) false
Ans-a
- 2 marks question
1) Point (4, 5) lies on the graph of the equation 3y = kx + 7. The value of k is:
Ans-
3y = kx + 7
Here, x = 4 and y = 5
Hence,
(3×5) = (kx4) + 7
15 = 4k+7
4k = 15–7
4k = 8
K = 2
2) 2x – 5y = 7 is linear equation. Explain.
Ans=>
The linear equation 2x-5y has infinitely many solutions. Because, the equation 2x-5y = 7 is a equation, that involves two variables. Hence, for different values of x, we will get different values of y and vice-versa.
3) Find the value of k for which x = 0, y = 8 is a solution of 3x – 5y = k.
Ans=>
Since x = 0 and y = 8 is a solution of given equation
3x – 5y = k
3(0) – 5(8) = k
k = -40
4) Find ‘a’, if linear equation 2x – ay = 12 has one solution as (4, 2).
Ans=>
Since (4, 2) is a solution of given equation
2(4) – a(2) = 12
8 – 2a = 6
2 a = 6-8
a =-2/-2
Hence, a = 1
- Express x in term of y:
5x + 3y = 6
Ans=
Given equation is
5x+ 3y = 6
5x = 6 – 3y
Thus, x = 5(6 – 2y).
5) In figure a line find out the values of x.
Ans=>
Given that,
AOC is a line.
AOC=180°
Therefore, 40°+3x+2x=180°
5x=180°-40°
5x=140°
X=140/5
X= 28°
6) Express x in term of y : x/5 + 3y = 9
Ans=> the given equation is
x/5+3y=9
x/5=9-3y
Thus, x=5(9-3y)
7) Express 2x/7 – 5y = -6 in the form of ax + by + c = 0
Ans=
Given equation is 2x/7-5y=-6
2x-35y+42=0 which is the form of ax + by + c = 0
8) Find the value of k for which x = 2, y = 4 is a solution of 4x – 3y = k.
Ans=>
4x -3y=k
4(2)-3(4) =k
8-12=k
k=-4
9) If the temperature is – 60°C, then what is the temperature in Fahrenheit?
Solution:
Given linear equation is
F = (9/5)C + 32°
Put C = -60°, we have
F = 9/5(-60°) + 32°
F = – 108° + 32°
F= -140°
- 5 marks question
1) Express the following linear equations in the form ax + by + c = 0 and find out the values of a, b and c in each case:
a) 2x – y/4 – 10 = 0
b) -3x+5y = 6
c) y – 6 = 0
Ans=>
a) The equation x-y/5-10 = 0 can be written as:
(4)x + (-1/4) y + (-10) = 0
Now compare the above equation with ax + by + c = 0
Thus, we get;
a = 4
b = -1/4
c = -10
b) –3x + 5y = 6
Re-arranging the given equation, we get,
–3x + 5y – 6 = 0
The equation –3x + 5y – 6 = 0 can be written as,
(–3)x + 5y +(– 6) = 0
Now comparing (–3)x + 5y +(– 6) = 0 with ax + by + c = 0
We get, a = –3
b = 5
c = -6
c) y – 6 = 0
Solution:
y – 6 = 0
The equation y – 6= 0 can be written as,
0x + 1y + (–6) = 0
Now comparing 0x + 1y + (–6) = 0with ax + by + c = 0
We get, a = 0
b = 1
c = –6
2) If the point (3, 4) lies on the graph of the equation 2y = ax + 8, find the value of a.
Ans=>
The given equation is
2y = ax + 8
According to the question, x = 3 and y = 4
Now, Substituting the values of x and y in the equation 2y = ax + 8,
We get,
(2×4) = (ax3) + 8
8 = 3a+8
3a = 12–8
3a = 4
a = 4/3
The value of a, if the point (3, 4) lies on the graph of the equation 2y = ax + 8is 4/3.
3) Draw the graph of x + y = 8
Ans=>
x + y = 8
y = 8 – x
at x=0 then y=8-0
y= 8
at x=8 then y=8-8
y=0
(0, 8) and (8, 0) are the solution
We can use the following table to draw the graph
X |
0 | 8 |
Y | 8 |
0 |
Origin |
0 |
0 |