Question #7c1f2

1 Answer
Dec 7, 2017

$x = - 3$

$y = 1$

Explanation:

We don’t need to manipulate this system of equations, the $y$ terms are already opposites, meaning they will cancel out—eliminate—when the equations are added.

So just add the equations:

$\setminus \quad 2 x + \cancel{y} = - 5$
+$3 x - \cancel{y} = - 10$
._________

$\setminus \implies 5 x = - 15$

$\therefore x = - 3$

Plug $x$ into one equation to solve for $y$:

$2 x + y = - 5$

$\setminus \implies 2 \left(- 3\right) + y = - 5$

$\setminus \implies - 6 + y = - 5$

$\setminus \therefore y = 1$

Check the answers by plugging both into an equation:

$3 x - y = - 10$

$\setminus \implies 3 \left(- 3\right) - 1 = - 10$

$\setminus \implies - 9 - 1 = - 10$

$\implies - 10 = - 10$

So the answer is correct.