# How do you solve the following system?:  x - 3y = 0 , -3x + 7y = 1

Jun 17, 2016

$x = - 1 \frac{1}{2} , \mathmr{and} y = \frac{- 1}{2}$

#### Explanation:

In order to work with these simultaneous equations, I will make the coefficients of the x terms both 3. But it will be easier to have them as additive inverses, (because by adding: -3 +3 = 0)

$\text{ "x - 3y = 0 " A}$
$\text{ "-3x + 7y = 1 " B}$

A x 3: $\text{ "3x - 9y = 0" } C$

B+C: $\text{ " -2y = 1 " the x-terms have been eliminated}$
$\text{ } y = - \frac{1}{2}$

If $y = - \frac{1}{2} , \text{ subst in A to find x}$

$x - 3 \left(\frac{- 1}{2}\right) = 0$

$x + \frac{3}{2} = 0$

$x = - \frac{3}{2}$