How do solve the following linear system?: -3x + 7y= -16 , x - 3y = -6 ?

May 16, 2018

$x = 45$, $y = 17$

Explanation:

From the second equation, you have $x = 3 y - 6$. Substitute this expression for $x$ in the first equation to get

$- 3 x + 7 y = - 16$

$\setminus \therefore - 3 \left(3 y - 6\right) + 7 y = - 16$

$\setminus \therefore - 9 y + 18 + 7 y = - 16$

$\setminus \therefore - 2 y = - 34$

$\setminus \therefore y = 17$

Once $y$ is known, we can derive $x$:

$x = 3 y - 6 \setminus \implies x = 3 \cdot 17 - 6 = 51 - 6 = 45$