How do solve the following linear system?: $- 3 x + 7 y = - 1, - x + 3 y = - 5$ $-3x+7y=-1 , -x+3y=-5$ ?

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Answer 1 · 2015-12-04T16:10:58

The solution for the system of equations is
$x = - 16, y = - 7$ $color(blue)(x=-16,y=-7$

$- 3 x + 7 y = - 1$ $-3x+7y=-1$ ......equation $1$ $1$

$- x + 3 y = - 5$ $-x+3y=-5$
$x = 3 y + 5$ $color(blue)(x=3y+5$ ..................equation $2$ $2$

Solving by substitution :

Substituting equation $2$ $2$ in equation $1$ $1$ :

$- 3 x + 7 y = - 1$ $-3x+7y=-1$

$- 3 \cdot (3 y + 5) + 7 y = - 1$ $-3 * (color(blue)(3y+5))+7y=-1$

$(- 3) \cdot (3 y) + (- 3) \cdot (5) + 7 y = - 1$ $(-3) * (3y) + (-3) * (5)+7y=-1$

$- 9 y - 15 + 7 y = - 1$ $-9y -15+7y=-1$

$- 9 y + 7 y = - 1 + 15$ $-9y +7y=-1 +15$

$- 2 y = 14$ $-2y=14$

$y = - \frac{14}{2}$ $y=-14/2$

$y = - 7$ $color(blue)(y=-7$

Finding $x$ $x$ by substituting $y$ $y$ in equation $2$ $2$

$x = 3 y + 5$ $color(blue)(x=3y+5$

$x = 3 \cdot (- 7) + 5$ $x=3 * (-7)+5$

$x = - 21 + 5$ $x=-21+5$

$x = - 16$ $color(blue)(x=-16$

The solution for the system of equations is
$x = - 16, y = - 7$ $color(blue)(x=-16,y=-7$

How do solve the following linear system?: −3x+7y=−1,−x+3y=−5 -3x+7y=-1 , -x+3y=-5 ?