How do you solve the following system?: $- x - 3 y = 5, - 3 x + 4 y = - 7$ $-x -3y =5, -3x +4y = -7$

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Answer 1 · 2016-03-31T17:21:52

The solution for the system of equations is:
$x = \frac{1}{13}$ $color(green)( x = 1/13$

$y = - \frac{22}{13}$ $color(green)(y = -22/13$

$- x - 3 y = 5$ $-x - 3y = 5$ , multiplying by $3$ $3$
$- 3 x - 9 y = 15$ $color(blue)(-3x) - 9y = 15$ ......equation $(1)$ $(1)$

$- 3 x + 4 y = - 7$ $color(blue)(-3x) + 4y =-7$ ......equation $(2)$ $(2)$

Solving by elimination.

Subtracting equation $(2)$ $(2)$ from $(1)$ $(1)$

$cancelcolor(blue)(-3x) - 9y = 15$

$cancelcolor(blue)(+3x) - 4y =+7$

$-13y = 22$

$color(green)(y = -22/13$

Finding $x$ from equation $1$

$-x - 3y = 5$

$x = - 3y - 5$

$x = - 3 * (color(green)( -22/13)) - 5$

$x = 66/13 - 5$

$x = 66/13 - 65/13$

$color(green)( x = 1/13$

How do you solve the following system?: -x -3y =5, -3x +4y = -7−x−3y=5,−3x+4y=−7-x -3y =5, -3x +4y = -7