Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x - 5 y - 11 = 0 2 x + 3 y + 4 = 0

Given, x - 5 y - 11 = 0 a 1 = 1 , b 1 = - 5 , c 1 = - 11 2 x + 3 y + 4 = 0 a 2 = 2 , b 2 = 3 , c 2 = 4 ∴ a 1 a 2 = 1 2 , b 1 b 2 = - 5 3 and c 1 c 2 = - 11 4 Here, a 1 a 2 ≠ b 1 b 2 From above comparison, the graphical interpretation is intersecting lines. Hence, algebraic interpretation is exact one solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x - 5 y - 11 = 0 2 x + 3 y + 4 = 0 1 2 - 5 3 - 11 4 a 1 a 2 ≠ b 1 b 2 Intersecting lines One solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algeb raic interpretation 2 x + 3 y = 6 3 x - 5 2 y - 2 = 0

Given, 2 x + 3 y = 6 ⇒ 2 x + 3 y - 6 = 0 a 1 = 2 , b 1 = 3 , c 1 = - 6 And 3 x - 5 2 y - 2 = 0 a 2 = 3 , b 2 = - 5 2 , c 2 = - 2 ∴ a 1 a 2 = 2 3 , b 1 b 2 = 3 - 5 2 = 6 - 5 and c 1 c 2 = - 6 - 2 = 3 1 Here, a 1 a 2 ≠ b 1 b 2 From above comparison, the graphical interpretation is intersecting lines. Hence, algebraic interpretation is exactly one solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algeb raic interpretation 2 x + 3 y = 6 3 x - 5 2 y - 2 = 0 2 3 6 - 5 3 1 a 1 a 2 ≠ b 1 b 2 Intersecting lines Exact one solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 2 x + y - 6 = 0 x - 2 y + 2 = 0

Given, 2 x + y - 6 = 0 a 1 = 2 , b 1 = 1 , c 1 = - 6 And x - 2 y + 2 = 0 a 2 = 1 , b 2 = - 2 , c 2 = 2 ∴ a 1 a 2 = 2 1 = 2 , b 1 b 2 = 1 - 2 = - 1 2 and c 1 c 2 = - 6 2 = - 3 Here, a 1 a 2 ≠ b 1 b 2 From above comparison, the graphical interpretation is intersecting lines. Hence, algebraic interpretation is exactly one solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 2 x + y - 6 = 0 x - 2 y + 2 = 0 2 - 1 2 - 3 a 1 a 2 ≠ b 1 b 2 Intersecting lines Exactly one solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 4 x + 2 3 y - 1 = 0 6 x - y - 2 = 0

Given, 4 x + 2 3 y - 1 = 0 a 1 = 4 , b 1 = 2 3 , c 1 = - 1 And 6 x - y - 2 = 0 a 2 = 6 , b 2 = - 1 , c 2 = - 2 ∴ a 1 a 2 = 4 6 = 2 3 b 1 b 2 = 2 3 - 1 = - 2 3 c 1 c 2 = - 1 - 2 = 1 2 Here, a 1 a 2 ≠ b 1 b 2 From above comparison, the graphical representation is intersecting lines. Hence, algebraic interpretation is exactly one solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 4 x + 2 3 y - 1 = 0 6 x - y - 2 = 0 2 3 - 2 3 1 2 a 1 a 2 ≠ b 1 b 2 Intersecting lines Exactly one solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x + 2 y - 3 = 0 5 x + 10 y + 1 = 0

Given, x + 2 y - 3 = 0 a 1 = 1 , b 1 = 2 , c 1 = - 3 And 5 x + 10 y + 1 = 0 a 2 = 5 , b 2 = 10 , c 2 = 1 ∴ a 1 a 2 = 1 5 b 1 b 2 = 2 10 = 1 5 c 1 c 2 = - 3 1 = - 3 Here, a 1 a 2 = b 1 b 2 ≠ c 1 c 2 From above comparison, the graphical representation is parallel lines. Hence, algebraic interpretation is no solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x + 2 y - 3 = 0 5 x + 10 y + 1 = 0 1 5 1 5 - 3 a 1 a 2 = b 1 b 2 ≠ c 1 c 2 Parallel lines No solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x - y + 1 = 0 - x + y + 1 = 0

Given, x - y + 1 = 0 a 1 = 1 , b 1 = - 1 , c 1 = 1 And - x + y + 1 = 0 a 2 = - 1 , b 2 = 1 , c 2 = 1 ∴ a 1 a 2 = 1 - 1 = - 1 b 1 b 2 = - 1 1 = - 1 c 1 c 2 = 1 1 = 1 Here, a 1 a 2 = b 1 b 2 ≠ c 1 c 2 From above comparison, the graphical interpretation is parallel lines. Hence, algebraic interpretation is no solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation x - y + 1 = 0 - x + y + 1 = 0 1 - 1 - 1 1 1 1 a 1 a 2 = b 1 b 2 ≠ c 1 c 2 Parallel lines No solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 6 x + 9 y = 12 3 x + 3 y = 6

Given, 6 x - 9 y = 12 ⇒ 6 x + 9 y - 12 = 0 a 1 = 6 , b 1 = 9 , c 1 = - 12 And 3 x - 3 y = 6 ⇒ 3 x - 3 y - 6 = 0 a 2 = 3 , b 2 = - 3 , c 2 = - 6 ∴ a 1 a 2 = 6 3 = 2 , b 1 b 2 = 9 - 3 = - 3 and c 1 c 2 = - 12 - 6 = 2 Here, a 1 a 2 ≠ b 1 b 2 From above comparison, the graphical interpretation is intersecting lines. Hence, algebraic interpretation is exactly one solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 6 x + 9 y = 12 3 x + 3 y = 6 6 3 9 - 3 - 12 - 6 a 1 a 2 ≠ b 1 b 2 Intersecting lines Exactly one solution

Here, a 1 , b 1 , c 1 and a 2 , b 2 , c 2 denote the coefficients of linear equations given below. Complete the following table: Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 25 x + 7 y = 12 100 x + 28 y = 7

Given, 25 x + 7 y = 12 ⇒ 25 x + 7 y - 12 = 0 And 100 x + 28 y = 7 ⇒ 100 x + 28 y - 7 = 0 ∴ a 1 a 2 = 25 100 = 1 4 b 1 b 2 = 7 28 = 1 4 c 1 c 2 = - 12 - 7 Here, a 1 a 2 = b 1 b 2 ≠ c 1 c 2 From above comparison, the graphical interpretation is parallel lines. Hence, algebraic interpretation is no solution. Pair of lines a 1 a 2 b 1 b 2 c 1 c 2 Compare the ratio Graphical representation Algebraic interpretation 25 x + 7 y = 12 100 x + 28 y = 7 1 4 1 4 - 12 - 7 a 1 a 2 = b 1 b 2 ≠ c 1 c 2 Parallel lines No solution

A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment)

Author:A P Singh

A P Singh Mathematics Solutions for Exercise - A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment)

Attempt the practice questions on Chapter 3: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment) with hints and solutions to strengthen your understanding. DINESH LAB MANUAL IN MATHEMATICS CLASS X solutions are prepared by Experienced Embibe Experts.

Questions from A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment) with Hints & Solutions

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (iii)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$x - 5 y - 11 = 0$ $2 x + 3 y + 4 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (iv)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$2 x + 3 y = 6$ $3 x - \frac{5}{2} y - 2 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (v)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$2 x + y - 6 = 0$ $x - 2 y + 2 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (vi)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$4 x + \frac{2}{3} y - 1 = 0$ $6 x - y - 2 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (vii)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$x + 2 y - 3 = 0$ $5 x + 10 y + 1 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (viii)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$x - y + 1 = 0$ $- x + y + 1 = 0$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (ix)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$6 x + 9 y = 12$ $3 x + 3 y = 6$

EASY

10th CBSE

IMPORTANT

DINESH LAB MANUAL IN MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>WORKSHEET (Self Assessment)>Q (x)

Here, $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ denote the coefficients of linear equations given below. Complete the following table:

Pair of lines	$\frac{a_{1}}{a_{2}}$	$\frac{b_{1}}{b_{2}}$	$\frac{c_{1}}{c_{2}}$	Compare the ratio	Graphical representation	Algebraic interpretation
$25 x + 7 y = 12$ $100 x + 28 y = 7$

A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment)

A P Singh Mathematics Solutions for Exercise - A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment)

Questions from A P Singh Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: WORKSHEET (Self Assessment) with Hints & Solutions

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