Grade 9 : Mathematics - 12. Linear Equations (Set 1)

Question 1

The standard form of a linear equation in two variables $x$ and $y$ is:

Accepted Answer

A) $ax + by + c = 0$, where a, b, c are real numbers and $a, b 
eq 0$

Answer

B) $ax^2 + by + c = 0$

Answer

C) $ax + b = 0$

Answer

D) $ax^2 + by^2 + c = 0$

Question 2

How many solutions does a linear equation in two variables, such as $2x + 3y = 6$, have?

Accepted Answer

C) Infinitely many solutions

Answer

A) Exactly one solution

Answer

B) Exactly two solutions

Answer

D) No solution

Question 3

Is the ordered pair $(2, 3)$ a solution to the linear equation $x + y = 5$?

Accepted Answer

A) Yes, $(2, 3)$ is a solution

Answer

B) No, $(2, 3)$ is not a solution

Answer

C) It depends on the scale

Answer

D) Insufficient information

Question 4

Find the value of $k$ if $x = 2, y = 1$ is a solution of the equation $2x + 3y = k$.

Accepted Answer

C) 7

Answer

A) 5

Answer

B) 6

Answer

D) 8

Question 5

The equation representing the x-axis in the Cartesian plane is:

Accepted Answer

B) $y = 0$

Answer

A) $x = 0$

Answer

C) $x = y$

Answer

D) $x + y = 0$

Question 6

The equation representing the y-axis in the Cartesian plane is:

Accepted Answer

A) $x = 0$

Answer

B) $y = 0$

Answer

C) $x = 1$

Answer

D) $y = 1$

Question 7

The graph of the linear equation $x = 4$ is a straight line:

Accepted Answer

B) Parallel to the y-axis

Answer

A) Parallel to the x-axis

Answer

C) Passing through the origin

Answer

D) Passing through $(0, 4)$

Question 8

The graph of the linear equation $y = -3$ is a straight line:

Accepted Answer

A) Parallel to the x-axis

Answer

B) Parallel to the y-axis

Answer

C) Passing through $(0, 0)$

Answer

D) Perpendicular to the x-axis

Question 9

If the point $(a, 4)$ lies on the line $3x + y = 10$, what is the value of $a$?

Accepted Answer

B) 2

Answer

A) 1

Answer

C) 3

Answer

D) 4

Question 10

Express $3x - 5y = 7$ in standard form $ax + by + c = 0$ and find the value of $c$.

Accepted Answer

B) -7

Answer

A) 7

Answer

C) 5

Answer

D) -5

Question 11

Any point on the line $y = x$ has coordinates of the form:

Accepted Answer

C) $(a, a)$

Answer

A) $(a, 0)$

Answer

B) $(0, a)$

Answer

D) $(a, -a)$

Question 12

Any point lying on the x-axis is of the form:

Accepted Answer

A) $(a, 0)$

Answer

B) $(0, a)$

Answer

C) $(a, a)$

Answer

D) $(0, 0)$ only

Question 13

Any point lying on the y-axis is of the form:

Accepted Answer

B) $(0, a)$

Answer

A) $(a, 0)$

Answer

C) $(a, a)$

Answer

D) $(-a, a)$

Question 14

Which of the following points lies on the line $2x + y = 4$?

Accepted Answer

A) $(1, 2)$

Answer

B) $(2, 1)$

Answer

C) $(0, 2)$

Answer

D) $(3, 1)$

Question 15

Find the coordinates of the point where the line $x + y = 6$ intersects the x-axis.

Accepted Answer

B) $(6, 0)$

Answer

A) $(0, 6)$

Answer

C) $(3, 3)$

Answer

D) $(6, 6)$

Question 16

Find the coordinates of the point where the line $2x + 3y = 12$ intersects the y-axis.

Accepted Answer

B) $(0, 4)$

Answer

A) $(6, 0)$

Answer

C) $(4, 0)$

Answer

D) $(0, 6)$

Question 17

If a linear equation passes through $(-2, 2)$, $(0, 0)$, and $(2, -2)$, its equation is:

Accepted Answer

B) $x + y = 0$

Answer

A) $y = x$

Answer

C) $x - y = 0$

Answer

D) $2x + y = 0$

Question 18

The cost of a notebook ($x$) is twice the cost of a pen ($y$). Which linear equation represents this statement?

Accepted Answer

A) $x - 2y = 0$

Answer

B) $2x - y = 0$

Answer

C) $x + 2y = 0$

Answer

D) $x + y = 2$

Question 19

Which of the following equations is satisfied by the point $(-3, 5)$?

Accepted Answer

A) $x + y = 2$

Answer

B) $x - y = 2$

Answer

C) $2x + y = 1$

Answer

D) $x + 2y = 5$

Question 20

How many solutions does the linear equation $y = 3x + 5$ have?

Accepted Answer

C) Infinitely many solutions

Answer

A) A unique solution

Answer

B) Only two solutions

Answer

D) No solution

Grade 9 : Mathematics - 12. Linear Equations (Set 1)