How do you solve the system $2 x - 9 y = 6$ $2x-9y=6$ and $4 x - 3 y = - 7$ $4x-3y=-7$ ?

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Answer 1 · 2015-07-24T14:02:58

The solution for the system of equations is:
$x = - \frac{27}{10}, y = - \frac{19}{15}$ $color(blue)(x=-27/10, y=-19/15$

$2 x - 9 y = 6$ $2x−9y=6$ , multiplying this equation by $2$ $2$

$4 x - 18 y = 12$ $color(blue)(4x)−18y=12$ ........equation $(1)$ $(1)$

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

Solving through elimination:

Subtracting equation $(1)$ $(1)$ from $(2)$ $(2)$ :
$color(blue)(cancel(4x)−3y=−7$
$color(blue)(cancel(-4x)+18y=-12$

$15y=-19$

$color(blue)(y=-19/15$

Finding $x$ from the first equation :

$2x−9y=6$

$2x=6+9y$

$x=(6+9y)/2$

$x=(6+9*(-19/5))/2$

$color(blue)(x=-27/10$

How do you solve the system 2x-9y=62x−9y=62x-9y=6 and 4x-3y=-74x−3y=−74x-3y=-7?