# How to solve simultaneous linear equations?

â€ŠSimultaneous linear equations or linear simultaneous equations:

• â€Šâ€ŠTwo 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. â€Š â€Š
• â€Š â€ŠFor example, â€Š $â€Š2x+3y-7 = 0$ and $x+2y-4=0$ is a system of linear equations. â€ŠThe solution of the above system of linear equations is (2,1).
â€ŠTo 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 $â€Š2x+3y-7=0$ from $2x+4y-8=0$, we get,

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

$y-1=0$

$y=1$

Substituting $y=1$ in $â€Š2x+3y-7=0$, 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 $(2,1)$.

Updated on: 10-Oct-2022

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