Solution of Simultaneous Linear Equation

Simplify:

$x+\frac{2}{y}= 7$

$2x-\frac{6}{y}= 9$

Solve for $x$ and $y$:

$4 x-3 y=18$

$4y-5x=-7$.

Solve using the comparative method:

$\frac{x}{3}+\frac{y}{4}=1$

$2x+4y=11$

If $\sqrt{a}-b+\sqrt{b}-c+\sqrt{c}-a=0$ then prove that $a=b=c$

Solve:

 $3x-\frac{2}{y}=5$; $x+\frac{4}{y}=4$

Solve: $\frac{2}{x}+\frac{{\displaystyle 5}}{y}=1; \frac{3}{x}+\frac{2}{y}=\frac{19}{30}$

Solve the following:

${\left(7x-3y-31\right)}^2+{\left(9x-5y-41\right)}^2=0$

The sum of the digits of a two-digit number is $9$. If $17$ is subtracted from the number, both the digits of the number become equal. Find the number.

Certain number of marbles were distributed equally among few boys. Had the number of boys been $2$ less, each boy would have got $3$ marbles more. Again had the number of boys been $6$ more each boy would have got $5$ marbles less. Find the number of boys and that of marbles.$$

Solve:

$$\begin{gathered} 3x-\frac{2}{y}=5 \\ x+\frac{4}{y}=4 \end{gathered}$$

A pair of linear equations can be consistent but cannot be inconsistent

A pair of linear equations which is consistent can be dependent but not Independent.

A pair of linear equations which is consistent can be dependent or Independent

A pair of linear equations can be consistent or inconsistent

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.
$x-y=3, \frac{x}{3}+\frac{y}{2}=6$

Two trains $100 \mathrm{m}$ and $80 \mathrm{m}$ long is running along the parallel rail lines. When they run in the same direction, then the train of faster speed crosses the train of slower speed in $18 \mathrm{seconds}$. And when they run in the opposite direction with equal speed, then they meet in $9 \mathrm{seconds}$. Find the speed of the two trains. 

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.

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