Practice the AP 9th Class Maths Bits with Answers Chapter 6 Linear Equation in Two Variables on a regular basis so that you can attempt exams with utmost confidence.
AP State Syllabus 9th Class Maths Bits 6th Lesson Linear Equation in Two Variables with Answers
Choose the correct answer :
Question 1.
An equation of the form ax + by + c = 0 is called a …………… equation.
A) linear
B) square
C) circular
D) rectangular
Answer:
A) linear
Question 2.
\(\frac{x}{3}+\frac{y}{4}=\frac{1}{24}\) in the form of ax + by + c = 0 is
A) 3x + 4y = 2
B) 4x + 3y = 2
C) 8x + 6y + 1 = 0
D) 8x + 6y – 1 = 0
Answer:
D) 8x + 6y – 1 = 0
Question 3.
The cost of a mango and a banana is 36, it can be expressed as
A) x – y = 36
B) x = 36 + y
C) x + y = 36
D) x + y + 36 = 0
Answer:
C) x + y = 36
Question 4.
The equation \(\sqrt{2} x=\sqrt{3} y+5\) in the form of ax + by + c = 0 is
A) \(\sqrt{2} x – \sqrt{3} y+5\)
B) \(\sqrt{2} x – \sqrt{3} y-5\)
C) \(\sqrt{2} x – \sqrt{3} y\) = 0
D) x – y – 5 = 0
Answer:
B) \(\sqrt{2} x – \sqrt{3} y-5\)
Question 5.
Comparing 5x – 6y = 10 with ax + by + c = 0, value of c is
A) 5
B) 6
C) 10
D) – 10
Answer:
D) – 10
Question 6.
Comparing 6x = 7y with linear equation, value of c is
A) 6
B) 7
C) 13
D) 0
Answer:
D) 0
Question 7.
Comparing x = \(\frac{7}{3}\) y with linear form, 3
A) 1
B) \(\frac{7}{3}\)
C) 3
D) 0
Answer:
C) 3
Question 8.
Comparing \(\frac{-\mathbf{x}}{8}=\frac{\mathbf{y}}{\mathbf{4}}\) with linear form,
A) \(\frac{-1}{2}\)
B) \(\frac{1}{8}\)
C) \(\frac{1}{4}\)
D) 2
Answer:
D) 2
Question 9.
\(\frac{8}{9}\) x = -y in linear form is
A) 8x + 9y = 0
B) 8x – 9y = 0
C) – 8x + 9y = 0
D) 8x – y = 9
Answer:
A) 8x + 9y = 0
Question 10.
“The sum of two numbers is 12″ in linear form
A) x – y = 12
B) x = 12
C) x = y + 12
D) x + y = 12
Answer:
D) x + y = 12
Question 11.
‘The difference between a number and twice the second number is 14’ in linear form
A) x + y = 14
B) x – y = 14
C) x + 2y=14
D) x – 2y – 14 = 0
Answer:
D) x – 2y – 14 = 0
Question 12.
‘Two angles x, y are supplementary”, in the linear form is
A) x + y – 90 = 0
B) x – y + 90 = 0
C) x + y – 180 = 0
D) x + y + 180 = 0
Answer:
C) x + y – 180 = 0
Question 13.
Any pair of values for which x and y satisfy the linear equation ax + by + c = 0 is called its
A) coefficients
B) solution
C) variable value
D) origin
Answer:
B) solution
Question 14.
If x = 2 then solution of 2x + 3y = 13 is
A) (2, 9)
B) (2, 3)
C) (3, 2)
D) (9, 2)
Answer:
B) (2, 3)
Question 15.
A linear equation has solutions.
A) one
B) two
C) three
D) many
Answer:
D) many
Question 16.
The number of solutions to 3x – 5y = 8 is
A) 1
B) 2
C) 4
D) many
Answer:
D) many
Question 17.
One solution to 5x + 3y – 22 = 0 is
A) (1,2)
B)(1, 1)
C) (2, 4)
D) (3, 4)
Answer:
C) (2, 4)
Question 18.
If x = 3 and y. = 3 is a solution of 2x – 3y – k = 0 then the value of k is
A) 3
B) – 3
C) 0
D) – 6
Answer:
B) – 3
Question 19.
If x = 0 and y = 1 is a solution of 5x – by + 3 = 0 then the value of b is
A) 1
B) 5
C) – 3
D) 3
Answer:
D) 3
Question 20.
The graph of a linear equation is a
A) straight line
B) circle
C) square
D) parabola
Answer:
A) straight line
Question 21.
The line of the form y = mx passes through is
A) (0, 0)
B) (2, 1)
C) (2, 2)
D) (0, 2)
Answer:
A) (0, 0)
Question 22.
Equation of a line parallel to X-axis is
A) x = 3
B) x = -5
C) y = 0
D) y = 3
Answer:
D) y = 3
Question 23.
Equation of a line parallel to Y-axis is
A) x = 8
B) x = 0
C) y = 0
D) y = – 5
Answer:
A) x = 8
Question 24.
If a point P lies on X-axis, then it may
A) (0,3)
B) (0, – 8)
C) (0, \(\frac { -1 }{ 2 }\) )
D) (5, 0)
Answer:
D) (5, 0)
Question 25.
Equation of X – axis is
A) x = 2
B) x = – 2
C) y = 0
D) y = 1
Answer:
C) y = 0
Question 26.
If (2, 2) is a solution of 3x + ay = 8, find ‘a’.
A) 2
B) 0
C) 6
D) 1
Answer:
D) 1
Question 27.
2015 x + 2016 y = 4031 represents a ………….
A) Straight line
B) Parabola
C) Curved line
D) Circle
Answer:
A) Straight line
Question 28.
From the equation 4x + y = 9, find ‘y’ if x = \(\frac { 9 }{ 4 }\)
A) 0
B) 9
C) 1
D) 2
Answer:
A) 0
Question 29.
The graph of x = k is a line parallel to Y – axis at a distance of k units and passing through the point
A) (0, k)
B) (0, 0)
C) (k, 0)
D) none of these
Answer:
C) (k, 0)
Question 30.
The graph of y = k is a line parallel to X – axis at a distance of k units and passing through the point
A) (k, 0)
B) (1, 1)
C) (0, 0)
D) (0, k)
Answer:
D) (0, k)
Question 31.
Equation of X – axis is
A) y – 1 = 0
B) y = 0
C) x = 0
D) x + y= l
Answer:
B) y = 0
Question 32.
Equation of Y – axis is
A) x – 1 = 0
B) x + y = 0
C) x = 0
D) y = 0
Answer:
C) x = 0
Question 33.
Which of the following points satisfy the equation x + 2y = 6 ?
A) (2,0)
B) (- 2, 0)
C) (0, 3)
D) (2, 3)
Answer:
C) (0, 3)
Question 34.
The point that does not lie on the line y = – x + 2 is
A) (- 1, – 1)
B) (2, 0)
C) (0, 2)
D) (- 1, 3)
Answer:
A) (- 1, – 1)
Question 35.
Write – 2x = \(\frac { -3 }{ 5 }\) y +1 in linear form
A) – 2x + 3y – 5 = 0
B) – 10x + 3y + 5 = 0
C) – 10x + 3y – 5 = 0
D) – 2x – 3y – 5 = 0
Answer:
C) – 10x + 3y – 5 = 0
Question 36.
Write 3x – 4y = 5 in the linear form
A) 3x – 4y – 5 = 0
B) 3x + 4y – 5 = 0
C) – 3x – 4y + 5 = 0
D) 3x + 4y + 5 = 0
Answer:
A) 3x – 4y – 5 = 0
Question 37.
The line which passes through the origin is
A) x + y = 3
B) y = 3x
C) x = 5
D) y = 4
Answer:
B) y = 3x
Question 38.
Which of the following is not a solution of 3x – y = 0 ?
A) (4, 12)
B) (6, 18)
C) (5, 15)
D) (- 3, 9)
Answer:
D) (- 3, 9)
Question 39.
The point which does not satisfy the equation x + y = 0 is mi i
A) (1,1)
B) (1, – 1)
C) (- 1, 1)
D)(-2,2)
Answer:
A) (1,1)
Question 40.
Given that x – 2y = 3. The value of ‘y’ in terms of ‘x’ is
A) \(\frac { x+3 }{ 2 }\)
B) \(\frac { x-3 }{ 2 }\)
C) \(\frac { -x+3 }{ 2 }\)
D) \(\frac { -x-3 }{ 2 }\)
Answer:
B) \(\frac { x-3 }{ 2 }\)
Question 41.
Which of the following is solution of the equation 2x – 5y = 10 ?
A) (0, 2)
B) (1/2, 2)
C) (3, – 1)
D) (0, – 2)
Answer:
D) (0, – 2)
Question 42.
Express the following statement as a linear equation in two variables. ‘The sum of two numbers is 24″.
A) x + 4y = 24
B) 4x + y = 24
C) x + y = 24
D) xy = 24
Answer:
C) x + y = 24
Question 43.
The equation \(\frac{x}{4}-\frac{y}{7}\) = 3 in linear form is
A) 4x – 7y – 84 = 0
B) 7x – 4y – 84 = 0
C) 4x + 7y – 84 = 0
D) 7x + 4y + 84 = 0
Answer:
B) 7x – 4y – 84 = 0
Question 44.
If (- 3, 2) is a solution of 5x – 8y + k = 0, then the value of k is
A) 15
B) 16
C) 31
D) 13
Answer:
C) 31
Question 45.
If (2, – 1) is a solution of 4x + by + 4 = 0, then the value of ‘b’ is
A) 12
B) 8
C) 4
D) – 12
Answer:
A) 12
Question 46.
A line parallel to X – axis is
A) y = – 3
B) x = 2
C) x + y = 5
D) y = 2x
Answer:
A) y = – 3
Question 47.
The number of solutions of 7x – 3y – 15 = 0 is
A) 2
B) 1
C) Infinite
D) 3
Answer:
C) Infinite
Question 48.
A line parallel to Y – axis is
A) x = 4
B) 2x – 3y + 1 = 0
C) y = 3
D) x = –\(\frac { 1 }{ 2 }\)y
Answer:
A) x = 4
Question 49.
The equation of a line parallel to X – axis and passing through (7, – 2) is
A) x = 7
B) y = -2
C) 7x + 2y = 0
D) 2x – 7y = 0
Answer:
B) y = -2
Question 50.
If x = 3, y = 2 is a solution of the equation 5x – 7y = k, then the value of ‘k’ is
A) 1
B) -11
C) 29
D) 31
Answer:
A) 1
Question 51.
If x = -3, y = -2 is a solution 5x – 7y = k, then the value of ‘k’
A) 0
B) 1
C) -1
D) 2
Answer:
C) -1
Question 52.
If x = 1, then the solution \(\frac{\mathbf{x}}{2}-\frac{\mathbf{y}}{\mathbf{3}}\) = 3 is
A) \(\left(1, \frac{-15}{2}\right)\)
B) \(\left(1, \frac{21}{2}\right)\)
C) \(\left(\frac{-15}{2}, 1\right)\)
D) \(\left(\frac{21}{2}, 1\right)\)
Answer:
A) \(\left(1, \frac{-15}{2}\right)\)
Question 53.
In this, which figure represents the y = -2?
Answer:
D)
Question 54.
If (\(\sqrt{5}\), – 3) is a solution of 75 x-V7y = k then the value of k is
A) 21
B) – 16
C) 16
D) 26
Answer:
D) 26
Question 55.
if the age of ‘x’ is 4 times of the age of ‘y’ then represent the information as a linear equation in two variables is….
A) x = 4y
B) y = 4x
C) y + 4x = 0
D) x + 4y = 0
Answer:
A) x = 4y
Question 56.
An auto charges Rs. 15/- for first kilometre and Rs. 8/- for each subsequent kilometre. If Prameela travelled 7 km., how much amount she would have paid ?
A) Rs. 105/-
B) Rs. 56/-
C) Rs. 71/-
D) Rs. 63/-
Answer:
D) Rs. 63/-
Question 57.
The distance of x = – 4 from the Y – axis is:…………..
A) 0 units
B) 1 unit
C) 4 units
D) – 4 units
Answer:
C) 4 units
Instructions : From the adjacent graph, answer the following questions (Q. No. 8-12) : In a school students prepared toilet cleaning acid by taking acid and water as shown in the graph. The quantity of acid taken and water are shown along X, Y axis respectively.
Question 58.
What is the scale factor used on X- axis?
A) 5 Units
B) 10 Units
C) 20 Units
D) 1 Unit
Answer:
C) 20 Units
Question 59.
Above given information represent as linear equation in two variables :
A) y = 3x
B) 3x = 4y
C) 4x = 3y
D) x = 3y
Answer:
A) y = 3x
Question 60.
If the quantity of acid is 20, then the quantity of water in units
A) 40
B) 20
C) 10
D) 60
Answer:
D) 60
Question 61.
In the diluted acid water quantity is 45, then the quantity of concentrated acid in units. [D]
A) 30
B) 90
C) 135
D) 15
Answer:
D) 15
Question 62.
What is the percentage of water in the diluted acid
A) 25
B) 33.3
C) 75
D) 20
Answer:
B) 33.3
Question 63.
Which of the following linear equations represent the co-ordinate points given in the table ?
A) 2y + 2 = x
B) 2x = y + 2
C) 2x – y = 2
D) 2x + 2 = y
Question 64.
The equation 2x + 5y = 7 has a unique solution, if x, y are
A) Positive real numbers
B) Real numbers
C) Rational numbers
D) Natural numbers
Answer:
D) Natural numbers
Question 65.
Statement (A) : A linear equation 2x + 3y = 5 has a unique solution.
Statement (B) : The line parallel to the Y-axis at a distance 4 units to the left of Y-axis is given by the equation x = -4.
Statement (C) : The graph of the equation y = mx + c passes through the origin. By the above statement which of the following are correct ?
A) B and C are true, A is false.
B) B and C are false, A is true.
C) B is true and A and C are false.
D) A and B are true. C is false.
Question 66.
Choose correct matching from column -1 to column – II.
A) i – Q, ii – S, iii – P
B) i – Q, ii – P, iii – R
C) i – Q, ii – P, iii – S
D) i – S, ii – R iii – P
Answer:
B) i – Q, ii – P, iii – R
Question 67.
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation C = \(\frac{\mathbf{5 F}-\mathbf{1 6 0}}{\mathbf{9}}\) What is the numerical value of temperature which is same in both the scale ?
A) 30°
B) -40°
C) 40°
D) -30°
Answer:
B) -40°
Question 68.
The autorikshaw fare in a city is charged ₹ 8 for the first kilometre and ₹ 4 per kilometre for subsequent dis-tance covered. If distance ‘x’ km and for charged ‘y\ then this information express as a linear equation in two variables is
A) y = 4 (x + 1)
B) y = 4x + 8
C) y = 4x – 8
D) y = 4(x – 1)
Answer:
B) y = 4x + 8
Question 69.
The graph of y = 6 is a line
A) Parallel to y-axis at a distance 6 units from the origin.
B) Making an intercept 6 on the x – axis.
C) Making an intercept 6 on both the axis.
D) Parallel to x – axis at a distance 6 units from the origin.
Answer:
D) Parallel to x – axis at a distance 6 units from the origin.
Question 70.
The point of the form (a, a) always lies on
A) y – axis
B) On the line y = x
C) On the line x + y = 0
D) x – axis
Answer:
B) On the line y = x
Question 71.
The graph of the linear equation 2x + 3y = 12 at what points cuts the X- axis and Y-axis ?
A) (0, 4), (6, 0)
B) (4, 0), (0, 6)
C) (0, 2), (3, 0)
D) (2, 0), (0, 3)
Answer:
A) (0, 4), (6, 0)
Question 72.
Which of the following graph represents the linear equation x + y = 0 ?
Answer:
B
Question 73.
Which of the following represent a line parallel to x-axis ?
A) 2x + y = 7-
B) 2y – 3 = y + 1
C) x + 3 = 0
D) x + y = 3
Answer:
B) 2y – 3 = y + 1
Question 74.
If (2,0) is a solution of the linear equa-tion 2x + 3y = K, then the value of K is
A) 4
B) 6
C) 5
D) 2
Answer:
A) 4
Question 75.
From the linear equation F = \(\frac { 9 }{ 5 }\) C + 32, the equal temperature (in Fahren Heat) to 30°C is
A) 63°
B) 68°
C) 72°
D) 86°
Answer:
D) 86°
Question 76.
The equation 2018x + 2019y = 0 represents a
A) Point
B) Line
C) Line segment
D) Circle
Answer:
B) Line