Embibe Experts Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: Exercise

If $\frac{2x+y+2}{5}=\frac{3x-y+1}{3}=\frac{3x+2y+1}{6}$, then

Half the perimeter of a rectangular garden, whose length is $4 m$ more than its width is $36 m$. Find the dimension of the garden.

Neha went to a sale to purchase some pants and skirts. When her friend asked how many of each she brought, she answered “The number of skirts are two less than twice the number of pants purchased. Also, the number of skirts is four less than three times the number of pants purchased”. Help her friend to find out how many skirts and pants Neha brought.

Solve simultaneous linear equations in two variables by the method of elimination.

$41x+53y=135, 53x+41y=147$

Solve simultaneous linear equations in two variables by the method of elimination.

$\frac{x}{2}+\frac{y}{3}=2, \frac{x}{4}+\frac{y}{2}=2$

Solve the following simultaneous linear equations in two variables by the method of substitution:  $x+y=a+b, ax-by=a^2-b^2$

Solve the following simultaneous linear equations in two variables by the method of substitution:  $ax+by=c^2, a^{2}x+b^{2}y=c^2$

Solve the following system of equations in $x$ and $y$:

$(a-b)x+(a+b)y=a^2-2ab-b^2, (a+b)(x+y)=a^2+b^2$