# How do you find the solution of the system of equations x-y=4 and x-3y= -6?

May 4, 2015

Solving by elimination and substitution:

$x - y = 4$........equation 1

multiplying this equation by '$- 1$' for elimination
$- x + y = - 4$ ...........equation 1
$x - 3 y = - 6$ ..............equation 2

on adding the two equations $x$ gets cancelled :
$- 2 y = - 10$ (minus signs cancel)
$y = \frac{10}{2}$ = 5

substituting this value of $y$ in equation 1:

$x - y = 4$
$x - 5 = 4$
$x = 9$

the solution for the system of equations are :
$\textcolor{b l u e}{x} = 9$
$\textcolor{b l u e}{y} = 5$