Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables – Exercise 3.1

 Introduction

Exercise 3.1 introduces the concept of linear equations in two variables. These are equations of the form:

$$$$ax+by+c=0

where $a,b,c$ are real numbers and $a,b\mathrm{\ne }0$. This exercise focuses on forming equations from word problems and representing them mathematically.

Formula Used

• General Form of Linear Equation in Two Variables:

$$$$ax+by+c=0

• Solution of Linear Equation: Any ordered pair $(x,y)$ that satisfies the equation.

NCERT Questions with Solutions (10)

Q1. Write the equation of a line parallel to x‑axis and passing through (0, 2).

Solution: Equation: $y=2$.

Q2. Write the equation of a line parallel to y‑axis and passing through (3, 0).

Solution: Equation: $x=3$.

Q3. Write the equation of a line passing through (0, 0) and slope 2.

Solution: Equation: $y=2x$.

Q4. Write the equation of a line passing through (0, 0) and slope $-3$.

Solution: Equation: $y=-3x$.

Q5. Write the equation of a line passing through (2, 3) with slope 1.

Solution: Equation: $y-3=1(x-2)$. Simplify: $y=x+1$.

Q6. Write the equation of a line passing through (1, -1) with slope 2.

Solution: Equation: $y+1=2(x-1)$. Simplify: $y=2x-3$.

Q7. Write the equation of a line passing through (0, 4) and slope $\frac{1}{2}$.

Solution: Equation: $y-4=\frac{1}{2}(x-0)$. Simplify: $y=\frac{1}{2}x+4$.

Q8. Write the equation of a line passing through (2, 5) and slope $-1$.

Solution: Equation: $y-5=-1(x-2)$. Simplify: $y=-x+7$.

Q9. Write the equation of a line passing through (3, -2) and slope $\frac{3}{4}$.

Solution: Equation: $y+2=\frac{3}{4}(x-3)$. Simplify: $y=\frac{3}{4}x-\frac{17}{4}$.

Q10. Write the equation of a line passing through (0, -3) and slope 5.

Solution: Equation: $y+3=5(x-0)$. Simplify: $y=5x-3$.

FAQs (10 from NCERT)

1. Q: What is a linear equation in two variables? A: An equation of the form $ax+by+c=0$.

2. Q: What is the solution of a linear equation? A: An ordered pair $(x,y)$ that satisfies the equation.

3. Q: How many solutions does a linear equation in two variables have? A: Infinitely many solutions.

4. Q: What is the slope of a line? A: The ratio of change in $y$ to change in $x$.

5. Q: What is the equation of a line parallel to x‑axis? A: $y=k$.

6. Q: What is the equation of a line parallel to y‑axis? A: $x=k$.

7. Q: What is the intercept form of a line? A: $\frac{x}{a}+\frac{y}{b}=1$.

8. Q: What is the slope‑intercept form of a line? A: $y=mx+c$.

9. Q: What is the point‑slope form of a line? A: $y-y_1=m(x-x_1)$.

10. Q: Why is this exercise important? A: It helps in forming equations from real‑life situations and graphing lines.

Conclusion

Exercise 3.1 has 10 solved questions and 10 FAQs that strengthen your understanding of forming linear equations in two variables and representing them mathematically. This builds the foundation for solving pairs of linear equations in Class 10 Maths.

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