Find the value of the following determinant 4 3 2 7

Given, 4 3 2 7 a d - b c is the value of determinant a b c d a b c d is a determinant. ( a , b ) , ( c , d ) are rows and a c , b d are columns. Thus, we have 4 3 2 7 = 4 × 7 - 3 × 2 = 28 - 6 = 22

Solve the following simultaneous equations. 7 x - 2 y x y = 5 ; 8 x + 7 y x y = 15

Given: 7 x - 2 y x y = 5 ; 8 x + 7 y x y = 15 7 x - 2 y x y = 5 ⇒ 7 x x y - 2 y x y = 5 ⇒ 7 y - 2 x = 5 and 8 x + 7 y x y = 15 ⇒ 8 x x y + 7 y x y = 15 ⇒ 8 y + 7 x = 15 Let 1 x = u , 1 y = v 7 v - 2 u = 5 . . . . . ( i ) 8 v + 7 u = 15 . . . . . . ii Multiply eq i with 7 and eq ii with 2 . 49 v - 14 u = 35 . . . . . . iii 16 v + 14 u = 30 . . . . . . ( iv ) Adding iii & iv 65 v = 65 ⇒ v = 1 And 1 y = v = 1 ⇒ y = 1 Putting the value of v in eq i 7 ( 1 ) - 2 u = 5 ⇒ u = 1 And 1 x = u = 1 ⇒ x = 1 ∴ ( x , y ) = ( 1 , 1 )

Solve the following simultaneous equations. 1 2 ( 3 x + 4 y ) + 1 5 ( 2 x - 3 y ) = 1 4 ; 5 ( 3 x + 4 y ) - 2 ( 2 x - 3 y ) = - 3 2

Given: 1 2 ( 3 x + 4 y ) + 1 5 ( 2 x - 3 y ) = 1 4 ; 5 ( 3 x + 4 y ) - 2 ( 2 x - 3 y ) = - 3 2 Let 1 3 x + 4 y = u & 1 2 x - 3 y = v 1 2 u + 1 5 v = 1 4 ⇒ 5 u + 2 v 10 = 1 4 ⇒ 10 u + 4 v = 5 . . . . . . i 5 u - 2 v = - 3 2 ⇒ 10 u - 4 v = - 3 . . . . . . ( ii ) On adding i & ii 20 u = 2 ⇒ u = 1 10 Putting the value of u in ii 10 × 1 10 - 4 v = - 3 ⇒ 1 + 3 = 4 v ⇒ v = 1 Since, 1 3 x + 4 y = u = 1 10 ⇒ 3 x + 4 y = 10 . . . . . . iii And 1 2 x - 3 y = v = 1 ⇒ 2 x - 3 y = 1 . . . . . . ( iv ) Multiply eq iii with 2 and iv with 3 6 x + 8 y = 20 . . . . . . ( v ) 6 x - 9 y = 3 . . . . . . vi Now eq v - vi 17 y = 17 ⇒ y = 1 Putting the value of y in vi 6 x - 9 = 3 ⇒ 6 x = 12 ⇒ x = 2 ∴ ( x , y ) = ( 2 , 1 )

Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set

Attempt the practice questions on Chapter 1: Linear Equations in Two Variables, Exercise 6: Problem Set with hints and solutions to strengthen your understanding. Algebra Standard X solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set with Hints & Solutions

EASY

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 4

Find the value of the following determinant
$|\begin{array}{l} 4 & 3 \\ 2 & 7 \end{array}|$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 6

Solve the following simultaneous equations.

$\frac{7 x - 2 y}{x y} = 5; \frac{8 x + 7 y}{x y} = 15$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 6

Solve the following simultaneous equations.

$\frac{1}{2 (3 x + 4 y)} + \frac{1}{5 (2 x - 3 y)} = \frac{1}{4}; \frac{5}{(3 x + 4 y)} - \frac{2}{(2 x - 3 y)} = - \frac{3}{2}$

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 7

Solve the following word problems.

A two-digit number and the number with digits interchanged add up to $143$ . In the given number the digit in the unit's place is $3$ more than the digit in the ten's place. Find the original number.

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 7

Kantabai bought $1 \frac{1}{2} kg$ tea and $5 kg$ sugar from a shop. She paid $₹ 50$ as return fare for rickshaw. Total expense was $₹ 700$ . Then she realised that by ordering online the goods can be bought with free home delivery at the same price. So next month she placed the order online for $2 kg$ tea and $7 kg$ sugar. She paid $₹ 880$ for that. Find the rate of sugar and tea per $kg$ .

HARD

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 7

Sum of the present ages of Manish and Savita is $31$ . Manish's age $3$ years ago was $4$ times the age of Savita. Find their present ages.

MEDIUM

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 7

In a factory the ratio of the salary of skilled and unskilled workers is $5 : 3$ . The total salary of one day of both of them is $₹ 720$ . Find daily wages of skilled and unskilled workers.

MEDIUM

10th Maharashtra Board

IMPORTANT

Algebra Standard X>Chapter 1 - Linear Equations in Two Variables>Problem Set>Q 7

Places $A$ and $B$ are $30 km$ apart and they are on a straight road. Hamid travels from $A$ to $B$ on bike. At the same time, Joseph starts from $B$ on bike, travels towards $A$ . They meet each other after $20$ minutes. If Joseph would have started from $B$ at the same time but in the opposite direction (instead of towards $A$ ) Hamid would have caught him after $3$ hours. Find the speed of Hamid and Joseph.

Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set

Questions from Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 6: Problem Set with Hints & Solutions

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