Solve the following pair of linear equations: i p x + q y = p - q q x - p y = p + q

Both equations can be written as: p x + q y - p - q = 0 … 1 q x - p y - p + q = 0 … 2 By using cross multiplication method, we get: x - q p + q - p ( p - q ) = y - q p - q + p ( p + q ) = 1 - p 2 - q 2 ⇒ x - p 2 - q 2 = y p 2 + q 2 = 1 - p 2 - q 2 Hence, x = 1 , y = - 1

Solve the following pair of linear equations. x a - y b = 0 , a x + b y = a 2 + b 2

x a - y b = 0 b x - a y = 0 … 1 a x + b y = a 2 + b 2 … 2 Multiplying equation 1 and 2 by b and a respectively, we get: b 2 x - a b y = 0 … 3 a 2 x + a b y = a 3 + a b 2 … 4 Adding equations 3 and 4 , we get: b 2 x + a 2 x = a 3 + a b 2 ⇒ x b 2 + a 2 = a a 2 + b 2 ⇒ x = a Substituting x in the equation 1 , we get: b a - a y = 0 a b - a y = 0 a y = a b y = b Hence, x = a , y = b

E M B I B E

MATHEMATICS - Class X>Chapter 3 - Pair of Linear Equations in Two Variables>Exercise 3.7

Exercise 3.7

Author:Jharkhand Board

Jharkhand Board Mathematics Solutions for Exercise 3.7

Simple step-by-step solutions to Exercise 3.7 questions of Pair of Linear Equations in Two Variables from MATHEMATICS - Class X. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from Exercise 3.7 with Hints & Solutions

HARD

10th Jharkhand Board

IMPORTANT

MATHEMATICS - Class X>Chapter 3 - Pair of Linear Equations in Two Variables>Exercise 3.7>Q 5

In a $∆ A B C, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B)$ . Find the three angles.

HARD

10th Jharkhand Board

IMPORTANT

MATHEMATICS - Class X>Chapter 3 - Pair of Linear Equations in Two Variables>Exercise 3.7>Q 6

Draw the graphs of the equations $5 x - y = 5$ and $3 x - y = 3$ . Determine the co-ordinates of the vertices of the triangle formed by these lines and the $y$ axis.