# How do you solve the system -x-7y=14 and  -4x-14y=28?

Jun 3, 2015

There are various approaches to solve a system of equations. One of the simplest ways is to eliminate one variable, solve for the other one and substituting it in the starting equations to solve for the eliminated variable.

Let us see how this works!

Given system of equation:

1. −x−7y=14
2. −4x−14y=28

Now, if we want to eliminate $x$, we need to multiply equation $1$ by 4 and subtract it from equation $2$.
Please note, there is no rule of thumb, and we can as well do the same for the other variable y.

However, we prefer to go for the variable where we don't need to multiply both equations by some factor to reach a set of equations with same co-efficient.

Coming back, multiplying equation $1$ by 4 gives,

3. −4x−28y=56
Subtracting the same from equation $2$ leaves us (Eqn. 2- Eqn. 3),
$14 y = - 28$
$\implies y = - 2$

Substituting y in either Eqn. 1 or Eqn. 2 gives us $x$

$- x - 7 \cdot - 2 = 14$
$\implies x = 0$

So, the system of equations solve as,
$x = 0 , y = - 2$

Verify your results by substituting the values in starting equations and check whether they match.