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## AP State Board 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