Algebraic Methods of Solving a Pair of Linear Equations

If $2x+3y=31$ and $7x=5y$, then what is the value of $2y-x$?

If$3x+7y=75$ and $5x-5y=25$. What is the value of $x+y$?

यदि $\mathrm{x}\times \mathrm{y}=\mathrm{x} +\mathrm{y} +1$ तथा $2\mathrm{p}\times 5\mathrm{p}=50$ हो तो p का मान होगा ?

If $3x-5y=5$ and $\frac{x}{x+y}=\frac{5}{7}$, then what is the value of $x-y$ ?

If $p^4+q^4+p^2{q}^2=273$ and $p^2+q^2-pq=21,$ then one of the values of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:

If $15p-12q= 69$, $12p-15q= 39$ then, find $p-q= ?$

If $3x-2y=4$ and $6x+7y=19$ the find the value of $x.$

$\sqrt{3}x+\sqrt{2}y=2\sqrt{2}; \sqrt{2}x-\sqrt{3}y=3\sqrt{3}$ implies $x=,y=$?

The cost of $2$ oranges and $3$ apples is $\mathrm{Rs}.28$. If the cost of an apple is doubled then the cost of $3$ oranges and $5$ apples is $\mathrm{Rs}.75$. The original cost of $7$ oranges and $4$ apples (in $\mathrm{Rs}.$) is

Solve the following system of equations by cross-multiplication method.
$$\begin{gathered} 2x + 3y + 8 = 0 \\ 4x + 5y + 14 = 0 \end{gathered}$$

Solve the following pair of linear equation by cross multiplication method:

$$\begin{gathered} 3x-4y=2 \\ y-2x=7 \end{gathered}$$

The cost of five chairs and three tables is $Rs 3110$. Cost of one chair is $Rs 210$less than the cost of one table. What is the cost of two tables and two chairs?

The point of intersection of lines $7x-15y-2=0$ and $6x+12y-18=0$ is

A number consists of two digits. The sum of both digits is $11$ . If  $27$added to the number then digits inter change their places. Find the number.

If $x=a, y=b$ is the solution of the equation $x-y=2$ and $x+y=4$ then the values of $a$ and $b$ are respectively

If$\mathrm{x}=2$, $\mathrm{y}=3$ is a solution of a pair of lines $2\mathrm{x}–3\mathrm{y}+\mathrm{a}=0$ and $2\mathrm{x}+3\mathrm{y}–\mathrm{b}+2=0$ then 

If $3x+y=10$ and $y=4$, then the value of $x$ is

Find the value of x and y and choose the option which depicts their relationship most appropriately.

$3x-2y=10$

$5x-6y=6$

Find the value of x, y, and z and choose the option which depicts their relationship most appropriately.

$7x+6y=110$

$4x+3y=59$

$x+z=15$

Find the value of x, y, and z and choose the option which depicts their relationship most appropriately.

${\left(x+y\right)}^3=1331$

$x-y+z=0$

$xy=28$