Grade 9 : Mathematics - 12. Linear Equations (Set 2)

Question 1

Write the linear equation $2x + 3y = 7$ in standard form $ax + by + c = 0$ and identify the values of $a$, $b$, and $c$.

Accepted Answer

A) $a = 2, b = 3, c = -7$

Answer

B) $a = 2, b = 3, c = 7$

Answer

C) $a = 3, b = 2, c = -7$

Answer

D) $a = -2, b = -3, c = -7$

Question 2

Which of the following ordered pairs is a solution of the equation $x - 2y = 4$?

Accepted Answer

C) $(4, 0)$

Answer

A) $(0, 2)$

Answer

B) $(2, 0)$

Answer

D) $(1, 1)$

Question 3

If $(2, k)$ is a solution of the linear equation $2x + 3y = 13$, find the value of $k$.

Accepted Answer

C) 3

Answer

A) 1

Answer

B) 2

Answer

D) 4

Question 4

What is the equation representing the x-axis in the Cartesian plane?

Accepted Answer

B) $y = 0$

Answer

A) $x = 0$

Answer

C) $x + y = 0$

Answer

D) $x = y$

Question 5

The graph of the linear equation $y = 3x$ passes through which of the following points?

Accepted Answer

B) $(1, 3)$

Answer

A) $(0, 3)$

Answer

C) $(3, 1)$

Answer

D) $(2, 3)$

Question 6

Any point on the line $y = x$ is always of the form:

Accepted Answer

C) $(a, a)$

Answer

A) $(a, 0)$

Answer

B) $(0, a)$

Answer

D) $(a, -a)$

Question 7

A taxi charges $10 for the first kilometer and $6 for each subsequent kilometer. Let the total distance covered be $x$ km and total fare be $$y$.

Which linear equation correctly models this situation?

Accepted Answer

A) $y = 6x + 4$

Answer

B) $y = 10x + 6$

Answer

C) $y = 6x + 10$

Answer

D) $y = 4x + 6$

Question 8

Find the value of $a$ if the point $(3, 4)$ lies on the graph of the equation $3y = ax + 7$.

Accepted Answer

A) $\frac{5}{3}$

Answer

B) $\frac{3}{5}$

Answer

C) $\frac{7}{3}$

Answer

D) $\frac{4}{3}$

Question 9

How many linear equations in $x$ and $y$ can be satisfied by the point $x = 1, y = 2$?

Accepted Answer

C) Infinitely many

Answer

A) Only one

Answer

B) Only two

Answer

D) None

Question 10

A linear equation in two variables $2x - 5y = 7$ has how many solutions?

Accepted Answer

C) Infinitely many solutions

Answer

A) A unique solution

Answer

B) Two solutions

Answer

D) No solution

Question 11

The graph of $x = 5$ is a line that is:

Accepted Answer

B) Parallel to the y-axis

Answer

A) Parallel to the x-axis

Answer

C) Passing through the origin

Answer

D) Lying along the x-axis

Question 12

Any point of the form $(a, -a)$ always lies on the line given by which equation?

Accepted Answer

C) $x + y = 0$

Answer

A) $x = a$

Answer

B) $y = -a$

Answer

D) $x - y = 0$

Question 13

The cost of a notebook is double the cost of a pen. Let $x$ be the cost of a notebook and $y$ be the cost of a pen.

Represent this statement as a linear equation in two variables.

Accepted Answer

B) $x - 2y = 0$

Answer

A) $x + 2y = 0$

Answer

C) $2x + y = 0$

Answer

D) $x - y = 2$

Question 14

At what point does the graph of $2x + 3y = 6$ intersect the x-axis?

Accepted Answer

B) $(3, 0)$

Answer

A) $(0, 2)$

Answer

C) $(2, 3)$

Answer

D) $(0, 3)$

Question 15

At what point does the graph of $3x + 4y = 12$ intersect the y-axis?

Accepted Answer

B) $(0, 3)$

Answer

A) $(4, 0)$

Answer

C) $(3, 0)$

Answer

D) $(0, 4)$

Question 16

If $x = 2, y = 1$ is a solution of the equation $2x + 3y = k$, what is the value of $k$?

Accepted Answer

C) 7

Answer

A) 5

Answer

B) 6

Answer

D) 8

Question 17

Which of the following equations represents a line passing through the origin $(0, 0)$?

Accepted Answer

B) $2x - 3y = 0$

Answer

A) $x + y = 1$

Answer

C) $x + 2 = 0$

Answer

D) $y - 5 = 0$

Question 18

How can the linear equation $y = 4$ be expressed in two variables $x$ and $y$?

Accepted Answer

B) $0 \cdot x + 1 \cdot y = 4$

Answer

A) $1 \cdot x + 1 \cdot y = 4$

Answer

C) $1 \cdot x + 0 \cdot y = 4$

Answer

D) $0 \cdot x + 0 \cdot y = 4$

Question 19

Yamini and Fatima, two Class 9 students, together contributed $100 towards a relief fund. Let Yamini's contribution be $$x$ and Fatima's contribution be $$y$.

Which equation models their total contribution?

Accepted Answer

A) $x + y = 100$

Answer

B) $x - y = 100$

Answer

C) $x + 100 = y$

Answer

D) $2x + y = 100$

Question 20

The formula converting Celsius ($C$) to Fahrenheit ($F$) is given by $F = \frac{9}{5}C + 32$.

If the temperature is $30^\circ ext{C}$, what is the temperature in Fahrenheit?

Accepted Answer

C) $86^\circ	ext{F}$

Answer

A) $76^\circ	ext{F}$

Answer

B) $82^\circ	ext{F}$

Answer

D) $94^\circ	ext{F}$

Grade 9 : Mathematics - 12. Linear Equations (Set 2)