Solve x 3 + y 4 = 4 and x 2 - y 4 = 1

Given, x 3 + y 4 = 4 ⇒ 4 x + 3 y 12 = 4 ⇒ 4 x + 3 y = 48 . . . . 1 Given, x 2 - y 4 = 1 ⇒ 4 x - 2 y 8 = 1 ⇒ 4 x - 2 y = 8 . . . . 2 Subtracting ( 2 ) from ( 1 ) , ⇒ 4 x + 3 y - 4 x - 2 y = 48 - 8 ⇒ 4 x + 3 y - 4 x + 2 y = 40 ⇒ 5 y = 40 ⇒ y = 8 Using this in 2 , ⇒ x 2 - 1 4 × 8 = 1 ⇒ x 2 - 2 = 1 ⇒ x 2 = 3 ⇒ x = 6 Hence, x = 6 and y = 8

Solve x 3 + 5 y = 13 and 2 x + y 2 = 19

Given, x 3 + 5 y = 13 ⇒ x + 15 y 3 = 13 ⇒ x + 15 y = 39 ⇒ x = 39 - 15 y . . . . 1 Also, given that 2 x + y 2 = 19 ⇒ 4 x + y 2 = 19 ⇒ 4 x + y = 38 . . . . 2 Substituting ( 1 ) in 2 , ⇒ 4 ( 39 - 15 y ) + y = 38 ⇒ 156 - 60 y + y = 38 ⇒ 59 y = 118 ⇒ y = 2 Putting this value in ( 2 ) , ⇒ x = 39 - 15 × 2 ⇒ x = 39 - 30 ⇒ x = 9 Hence, x = 9 and y = 2

Solve 2 x + 3 y = 13 and 5 x - 4 y = - 2

Given, 2 x + 3 y = 13 ⇒ 2 y + 3 x x y = 13 ⇒ 2 y + 3 x = 13 x y . . . . 1 5 x - 4 y = - 2 ⇒ 5 y - 4 x x y = - 2 ⇒ 5 y - 4 x = - 2 x y . . . . 2 Multiply equation ( 1 ) with 4 , ⇒ 8 y + 12 x = 52 x y . . . . 3 Multiply equation 2 with 3 , ⇒ 15 y - 12 x = - 6 x y . . . . 4 Adding equation ( 3 ) and ( 4 ) , ⇒ 8 y + 12 x + 15 y - 12 x = 52 x y - 6 x y ⇒ 23 y = 46 x y ⇒ 1 = 2 x ⇒ x = 1 2 Putting this in equation ( 1 ) , ⇒ 2 y + 3 1 2 = 13 1 2 y ⇒ 2 y + 3 2 = 13 2 y ⇒ 13 2 y - 2 y = 3 2 ⇒ 9 y 2 = 3 2 ⇒ y = 3 9 = 1 3 Hence, x = 1 2 and y = 1 3

E M B I B E

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set

Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 3: Problem set

Author:Maharashtra Board

Maharashtra Board Mathematics Solutions for Exercise - Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 3: Problem set

Attempt the practice questions on Chapter 5: Linear Equations in Two Variables, Exercise 3: Problem set with hints and solutions to strengthen your understanding. MHB - Math Part-I solutions are prepared by Experienced Embibe Experts.

Questions from Maharashtra Board Solutions for Chapter: Linear Equations in Two Variables, Exercise 3: Problem set with Hints & Solutions

MEDIUM

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -3

By equating coefficients of variables, solve $5 x + 7 y = 17$ and $3 x - 2 y = 4$

MEDIUM

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -3

By equating coefficients of variables, solve $x - 2 y = - 10$ and $3 x - 5 y = - 12$

MEDIUM

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -3

By equating coefficients of variables, solve $4 x + y = 34$ and $x + 4 y = 16$

MEDIUM

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -4

Solve $\frac{x}{3} + \frac{y}{4} = 4$ and $\frac{x}{2} - \frac{y}{4} = 1$

MEDIUM

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -4

Solve $\frac{x}{3} + 5 y = 13$ and $2 x + \frac{y}{2} = 19$

HARD

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -4

Solve $\frac{2}{x} + \frac{3}{y} = 13$ and $\frac{5}{x} - \frac{4}{y} = - 2$

HARD

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -5

A two-digit number is $3$ more than $4$ times the sum of its digits. If $18$ is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

HARD

9th Maharashtra Board

IMPORTANT

MHB - Math Part-I>Chapter 5 - Linear Equations in Two Variables>Problem set>Q -6

The total cost of $8$ books and $5$ pens is $₹ 420$ and the total cost of $5$ books and $8$ pens is $₹ 321$ . Find the cost of $1$ book and $2$ pens.