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

Dec 4, 2015

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

Explanation:

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

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

Solving by substitution :

Substituting equation $2$ in equation $1$:

$- 3 x + 7 y = - 1$

$- 3 \cdot \left(\textcolor{b l u e}{3 y + 5}\right) + 7 y = - 1$

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

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

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

$- 2 y = 14$

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

color(blue)(y=-7

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

color(blue)(x=3y+5

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

$x = - 21 + 5$

color(blue)(x=-16

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