# How do you determine the solution in terms of a system of linear equations for -5x-5y=5, -40x-3y=2?

May 18, 2018

$x = \frac{1}{37}$ and $y = - \frac{38}{37}$

#### Explanation:

$- 5 x - 5 y = 5$
$- 40 x - 3 y = 2$

Lets cancel out the $y$ terms to find $x$. Multiply the top equation by $- 3$ and the bottom equation by $- 5$ (multiply equations by opposite coefficients of $y$):

$\left(- 5 x \cdot - 3\right) - \left(5 y \cdot - 3\right) = 5 \cdot - 3$
$\left(- 40 x \cdot - 5\right) - \left(3 y \cdot - 5\right) = 2 \cdot - 5$

$15 x + 15 y = - 15$
$200 x + 15 y = - 10$

Subtract them from each other to eliminate $y$:

$- 185 x = - 5$
$x = - \frac{5}{-} 185$
$x = \frac{1}{37}$

Substitute $x = \frac{1}{37}$ back into one of the original equations (e.g. $- 5 x - 5 y = 5$) to find $y$:

$- 5 \left(\frac{1}{37}\right) - 5 y = 5$
$\left(- \frac{5}{37}\right) - 5 y = 5$
$- 5 y = 5 + \left(\frac{5}{37}\right)$
$- 5 y = \frac{190}{37}$
$y = \frac{\frac{190}{37}}{-} 5$
$y = - \frac{38}{37}$

Double check your results by substituting both values of $x$ and $y$ into an original equation and see whether the result is correct.