Solution of a Linear Equation

Draw the graph of the line $x-2y=3$. From the graph find the coordinates of the point when $x=-5$.

Draw the graph of the equation $y-x=2$.

If the point on the graph of the linear equation $2x+5y=19,$ whose ordinate is $1\frac{1}{2}$ times its abscissa, is $\left(a,b\right)$, find $(a+b)$.

$x=4, y=2$ is a solution of the linear equation

If $x=3k+2$ and $y=2k-1$ is a solution of the equation $4x-3y+1=0$, find the value of $k$.

Find the value of $k$ for which the point $(1,-2)$ lies on the graph of the linear equation $x-2 y+k=0.$

When any problem depends on different factors, then to solve these we need the concept of _____ equations and methods to solve it. 

Two places $A$ and $B$ are at $6 \mathrm{km}$ distance from each other. At the same time, two people start to run towards each other and meet in $45$ minutes. If they run in same direction, then they meet in $6$ hours. Find their speed.

In a city, a fixed charge and charge for a distance is included in the fare. If a passenger pays $₹105$ for $10 \mathrm{km}$ and $₹155$ for $15 \mathrm{km}$, then find the fixed charge and charge per $\mathrm{km}$.

 In a bus, the cost of $2$ tickets for stopage $A$ and $3$ tickets for stoppage $B$ is $₹46$, whereas the cost of $3$ tickets for stoppage $A$ and $5$ tickets for stoppage $B$ is $₹74$. Find the fare from stoppage $A$ to $B$.

Two cars are at $100 \mathrm{km}$ distant on a highway. If they start to run at the same time, then they meet in $5$ hours in the same direction an in $1$ hour in opposite direction. Their speeds are

If two people cover a distance of $7 \mathrm{km}$ in $3 \mathrm{hours}$ from the same place but different vehicles. If they go in the opposite direction, then the distance between them becomes $300 \mathrm{km}$ in the same time. Find the speed of their cars.

A train covers a specific distance with a constant speed. If it runs $10 \mathrm{km}/\mathrm{h}$ faster, then it takes $2$ hours less than the scheduled time. If it runs $10 \mathrm{km}/\mathrm{h}$ slower, then it takes $3$ hours more than the scheduled time. Find the distance in $\mathrm{km}$ covered by the train.

What is the present age of Ramesh (in years), if $10$ years ago he was $25$ years old?

Apoorv received three- fourths of all voted cast in the election for school president. If he received $876$ votes, then how many students voted?

Choose the equation whose graph is given below.

If $x=1, y=-1$ is a solution of equation $px-2y=10$, then find the value of $p$.

If $x=2$ and $y=1$is a solution of the equation $5x+8y=a$, then find the value of $a$.

If $(3 a-4,0)$ and $(5,0)$ are same points, then value of $a$ is

Ordered pair $(5, a)$ lies on the graph of $x+y=29$. Find the value of $a$.