How do you find the solution of the system of equations x + y = -7  and 3x + y = -9 ?

May 4, 2015

Solving by elimination and substitution:

$x + y = - 7$............................equation 1
$3 x + y = - 9$.........................equation 2

multiplying equation 1 by $- 1$ for elimination we get:
$- x - y = 7$

on adding the two equations $y$ gets cancelled
$- x - \cancel{y} = 7$
$3 x + \cancel{y} = - 9$

$2 x = - 2$

$x = - \frac{2}{2} = - 1$

substituting this value of $x$ in equation 1:
$x + y = - 7$
$- 1 + y = - 7$
$y = - 7 + 1$

$y = - 6$

the solution for the system of equations is:
$\textcolor{b l u e}{x} = - 1$
$\textcolor{b l u e}{y} = - 6$