How do solve the following linear system?:  -4x-15y=-1 , -3x+7y=-1 ?

Jul 31, 2016

The same values of $x$ and $y$ must satisfy both equations

Explanation:

Probably the easiest way to solve this is to manipulate the equations to bring them to a more convenient form in which both have the same coefficient for $x$. Multiply the fist one by $3$ and the second one by $4$:

$- 12 x - 45 y = - 3$
$- 12 x + 28 y = - 4$

This system is equivalent to the given one. Now we subtract the second form the first, and we get:
$- 73 y = 1$, and then $y = - \frac{1}{73}$. Now replacing the $y$ value in either equation, say the first one, we have:

$- 12 x - 45 \cdot \frac{1}{73} = - 3$, so

$- 12 x = - 3 + \frac{45}{73}$ so

$- 12 x = \frac{- 219 + 45}{73}$, and then

$- 12 x = - \frac{174}{73}$, and this results in

$x = \left(- \frac{1}{12}\right) \cdot \left(- \frac{174}{73}\right)$, and simplifying

$x = \frac{29}{146}$