Algebraic Methods of Solving a Pair of Linear Equations

If $x=3p$ and $y=\frac{2p}{5}+1$, then find the value of $p$ for which $x=5y$.

Express two simultaneous linear equations by drawing graphs.
$x-y=3, \frac{x}{3}+\frac{y}{2}=6$

Find the product of the value of $x$ and $y$ by solving the pair of equations $23x+29y=98, 29x+23y=110$.

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 $200 \mathrm{km}$, he pays $₹1050$. If the fixed charges per day is $₹x$ and the rate per $\mathrm{km}$ is $₹y$, then find the value of $x+y$ ?

Solve the following system of equations by the elimination method. Then, write the value of $x^2+y^2$ as final answer.

$$\begin{gathered} 2x+3y=46 \\ 3x+5y=74 \end{gathered}$$

The equations $x+y+1=0$ and $2x+2y+1=0$ have

Find the value of $x–y$ if $3x+2y=15, 2x+3y=10$.

For what value of $\text{'}t\text{'}$ the following pair of linear equations has a no solution? $2x-ty=5$ and $3x+2y=11$?

The solution of the pair of linear equations $2x+3y=8$ and $x+2y=5$ is

Sum of the areas of two squares is $850 {\mathrm{cm}}^2$. If the difference of their perimeters is $40 \mathrm{cm}$. Find the sides of the two squares.

Out of $555 \mathrm{km}$, Vishal travelled certain distance by bus and remaining distance by car. Bus travels with an average speed of $60 \mathrm{km}/\mathrm{hr}$ and the average speed of car is $75 \mathrm{km}/\mathrm{hr}$. He takes total $8 \mathrm{hours}$ to complete the journey. Find the distance that Vishal travelled by bus in $\mathrm{km}$.

Solve the following pair of linear equation by elimination method.

$3x+4y=10$ and $2x-2y=2$

The larger of two supplementary angles exceeds the smaller by $18°$. Then the angles are

The denominator of a fraction is $4$ more than twice its numerator. Denominator becomes $12$ times the numerator, if both the numerator and the denominator are reduced by $6$, find the fraction.

If $15x + 17y = 21$ and $17x + 15y = 11$, then find the value of $x + y.$

Find the value of variables which satisfies the following equation:

$2x+5y=20$

$3x+6y=12$

Find the solution of a pair of linear equation:

$y-2x=1$

$x+2y=12$

Solve the equation $\frac{x-2}{3}-\frac{2x-3}{2}=\frac{2x+3}{12}.$

In the given figure, $3\times \mathrm{CP}=\mathrm{PD}=9 \mathrm{cm}$ and $\mathrm{AP}=4.5 \mathrm{cm}.$ Find $\mathrm{BP}.$

On comparing the ratios $\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}, \frac{{\mathrm{b}}_1}{{\mathrm{b}}_2}$ and $\frac{{\mathrm{c}}_1}{{\mathrm{c}}_2}$, find out whether the below pair of linear equations is consistent or inconsistent.
$3x-y=2; 6x-2y=4$