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

The values of $a$ and $b$ for which the following system of equations has infinitely many solutions is 

\( 2x+3y=7\)

\( (a-b)x+(a+2)y=3a \)

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

Taxi charges in a city consist of fixed charges per day and the remaining depending upon the distance travelled in kilometres. If a person travels $110 \mathrm{km}$, he pays $₹690,$ and for travelling he pays $₹1050$. If the fixed charges per day is $₹x$ and the rate per km is $₹y$, then find the value of $x+y$ ?

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 $y$:

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