Important Questions for Class 9 Maths (Ganita Manjari II) Chapter 13 Two Variables, One Line 2026-27

Class 9 Maths Chapter 13 MCQs

1. Which equation is linear in two variables?

A. $$x^2+y=7$$
B. $$3x+2y=12$$
C. $$xy=6$$
D. $$x+y^2=9$$

Answer: B. $$3x+2y=12$$.

2. Which ordered pair is a solution of $$2x+3y=12$$?

A. $$(2,3)$$
B. $$(3,2)$$
C. $$(1,4)$$
D. $$(4,2)$$

Answer: B. $$(3,2)$$, because $$2(3)+3(2)=12$$.

3. What are the slope and y-intercept of $$y=-4x+7$$?

A. Slope = 4; y-intercept = 7
B. Slope = −4; y-intercept = −7
C. Slope = −4; y-intercept = 7
D. Slope = 7; y-intercept = −4

Answer: C. Slope = −4; y-intercept = 7.

4. Which statement correctly describes the graph of $$x=5$$?

A. It is horizontal and has zero slope.
B. It is vertical and has undefined slope.
C. It passes through the origin.
D. It is parallel to the x-axis.

Answer: B. It is vertical and has undefined slope.

5. If the graphs of two linear equations are distinct parallel lines, how many common solutions do the equations have?

A. Exactly one
B. Exactly two
C. Infinitely many
D. None

Answer: D. None.

Class 9 Maths Chapter 13 Very Short Answer Questions

6. State the standard form of a linear equation in two variables.

Answer: $$ax+by+c=0$$, where a, b and c are real numbers, and a and b are not both zero.

7. Find k if (2, 1) is a solution of $$2x+3y=k$$.

Solution:

Substitute x = 2 and y = 1:

$$k=2(2)+3(1)$$
$$k=4+3$$
$$k=7$$

Answer: k = 7.

8. Write any two solutions of $$x+y=6$$. How many solutions does this equation have over the real numbers?

Answer: 

Two solutions are (0, 6) and (2, 4). The equation has infinitely many solutions over the real numbers.

9. Find the slope and y-intercept of the line $$y=6$$.

Answer: 

The slope is 0 and the y-intercept is 6. Its graph is a horizontal line parallel to the x-axis.

Class 9 Maths Chapter 13 Short Answer Questions

10. Mangoes cost ₹60 per kg and bananas cost ₹50 per kg. Radha spends ₹280 on these fruits. Write a linear equation for this situation and check whether buying 3 kg of mangoes and 2 kg of bananas satisfies it.

Solution:

Let x and y represent the quantities of mangoes and bananas, in kilograms.

The total cost gives:

$$60x+50y=280$$

Dividing by 10:

$$6x+5y=28$$

Substitute x = 3 and y = 2:

$$6(3)+5(2)=18+10=28$$

Answer: The equation is $$6x+5y=28$$. Buying 3 kg of mangoes and 2 kg of bananas satisfies it.

11. Find the slope of the line passing through A(1, 3) and B(4, 9). Does the line rise or fall as x increases?

Solution:

$$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$$

$$\text{Slope}=\frac{9-3}{4-1}=\frac{6}{3}=2$$

Since the slope is positive, the line rises from left to right.

Answer: The slope is 2, and the line rises as x increases.

12. Express $$3x+2y-8=0$$ in slope-intercept form. Identify its slope and its points of intersection with both axes.

Solution:

$$3x+2y-8=0$$
$$2y=-3x+8$$
$$y=-\frac{3}{2}x+4$$

Comparing with $$y=mx+c$$:

Slope = $$-\frac{3}{2}$$
Y-intercept = 4

To find the y-axis intersection, substitute x = 0:

$$y=4$$

The y-axis intersection is (0, 4).

To find the x-axis intersection, substitute y = 0:

$$3x=8$$
$$x=\frac{8}{3}$$

The x-axis intersection is $$\left(\frac{8}{3},0\right)$$.

13. Solve the following pair of equations by substitution:

$$x+y=9$$
$$x-y=3$$

Solution:

From $$x-y=3$$:

$$x=y+3$$

Substitute into $$x+y=9$$:

$$(y+3)+y=9$$
$$2y+3=9$$
$$2y=6$$
$$y=3$$

Then:

$$x=3+3=6$$

Answer: x = 6 and y = 3.

14. Determine the number of solutions of each pair of equations. Give a reason.

(a) $$x+y=4$$ and $$2x+2y=8$$
(b) $$x+y=4$$ and $$x+y=7$$

Solution:

(a) Dividing the second equation by 2 gives:

$$x+y=4$$

Both equations represent the same line.

Answer: Infinitely many solutions.

(b) Rewrite the equations as:

$$y=-x+4$$
$$y=-x+7$$

The lines have the same slope, −1, but different y-intercepts. They are distinct and parallel.

Answer: No solution.

Class 9 Maths Chapter 13 Long Answer Questions

15. Solve the following pair of equations by elimination and verify your answer:

$$2x+3y=17$$
$$3x-2y=6$$

Solution:

Multiply the first equation by 2:

$$4x+6y=34$$ — (1)

Multiply the second equation by 3:

$$9x-6y=18$$ — (2)

Add equations (1) and (2):

$$13x=52$$
$$x=4$$

Substitute x = 4 into $$2x+3y=17$$:

$$2(4)+3y=17$$
$$8+3y=17$$
$$3y=9$$
$$y=3$$

Verification:

First equation:

$$2(4)+3(3)=8+9=17$$

Second equation:

$$3(4)-2(3)=12-6=6$$

Answer: x = 4 and y = 3.

16. Solve the following pair of equations graphically:

$$x+y=6$$
$$x-y=2$$

Solution:

For $$x+y=6$$, write $$y=6-x$$.

For $$x-y=2$$, write $$y=x-2$$.

The lines intersect at (4, 2).

Verification:

$$4+2=6$$
$$4-2=2$$

Answer: x = 4 and y = 2. The pair has exactly one solution.

17. A stationery shop charges ₹70 for 2 notebooks and 3 pens, and ₹80 for 3 notebooks and 2 pens. Find the price of one notebook and one pen.

Solution:

Let the price of one notebook be ₹x and one pen be ₹y.

According to the question:

$$2x+3y=70$$ — (1)
$$3x+2y=80$$ — (2)

Multiply equation (1) by 3:

$$6x+9y=210$$ — (3)

Multiply equation (2) by 2:

$$6x+4y=160$$ — (4)

Subtract equation (4) from equation (3):

$$5y=50$$
$$y=10$$

Substitute y = 10 into equation (1):

$$2x+3(10)=70$$
$$2x+30=70$$
$$2x=40$$
$$x=20$$

Verification:

Cost of 2 notebooks and 3 pens:

$$2(20)+3(10)=40+30=70$$

Cost of 3 notebooks and 2 pens:

$$3(20)+2(10)=60+20=80$$

Answer: One notebook costs ₹20, and one pen costs ₹10.

Tips to Solve Class 9 Maths Chapter 13 Two Variables, One Line Questions

Use these steps to form equations, plot graphs and check your solutions:

• Define the Variables: State what x and y represent in word problems.

• Check Signs: Handle negative signs carefully when rearranging equations.

• Choose a Suitable Method: Use substitution when a variable is easy to isolate and elimination when coefficients can be matched.

• Plot Points Accurately: Label both axes and use a consistent scale.

• Verify Both Equations: Substitute your answer into both original equations.

Benefits of Vedantu’s Class 9 Maths Chapter 13 Important Questions PDF

Vedantu’s Class 9 Maths Chapter 13 important questions with solutions support learning from Ganita Manjari Part II through clear, worked examples.

• Step-by-Step Solutions: Follow the reasoning behind algebraic and graphical methods.

• Concept Checks: Use Class 9 Maths Chapter 13 important questions MCQ practice to check your understanding of solutions, slopes and intercepts.

• Independent Learning: Compare your answers with the solutions and identify mistakes.

• Offline Access: Save the Class 9 Maths Chapter 13 important questions PDF to study and solve questions at your own pace.

Important Study Materials for Class 9 Maths (Ganita Manjari II) Chapter 13 Two Variables, One Line

CBSE Class 9 Maths Chapter-wise Important Questions

Other Important Related Links for CBSE Class 9 Maths