How to solve simultaneous linear equations?

 Simultaneous linear equations or linear simultaneous equations:

•   Two linear equations in two variables taken together are called simultaneous linear equations.
• The solution of system of simultaneous linear equation is the ordered pair (x, y) which satisfies both the linear equations.    
•    For example,   $ 2x+3y-7 = 0$ and $x+2y-4=0$ is a system of linear equations.  The solution of the above system of linear equations is (2,1).

 To solve we have to multiply one of the equations by any number such that its x or y coefficient becomes equal to the respective x or y coefficient of the other equation and subtract one equation from the other to find the values of x and y.

In the above example,

Multiplying $x+2y-4=0$ by 2, we get,

$2(x+2y-4)=2(0)$

$2x+4y-8=0$

Subtracting $ 2x+3y-7=0$ from $2x+4y-8=0$, we get,

$2x+4y-8-2x-3y-(-7)=0$

$y-1=0$

$y=1$

Substituting $y=1$ in $ 2x+3y-7=0$, we get,

$2x+3(1)-7=0$

$2x=7-3$

$x=\frac{4}{2}$

$x=2$

The solution of the system of linear equations is $(2,1)$.