How do you solve the system using elimination $y = - x + 5$ $y = -x + 5$ and $2 x - 3 y = - 6$ $2x - 3y = -6$ ?

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Answer 1 · 2015-06-03T08:01:05

$y = - x + 5$ $y = -x + 5$
$y + x = 5$ $y + x = 5$ .............equation $(1)$ $(1)$

$2 x - 3 y = - 6$ $2x color(red)(- 3y) = -6$ ...... equation $(2)$ $(2)$

multiplying equation $(1)$ $(1)$ by $3$ $3$
$(y + x = 5) \times 3$ $(y + x = 5) xx 3$

$3 x + 3 y = 15$ $3x color(red)(+3y) = 15$ ........ equation $(3)$ $(3)$

Adding equations $(2)$ $(2)$ and $(3)$ $(3)$ to eliminate $3 y$ $color(red)(3y$ :

$2x cancel(-3y) = -6$
$3x +cancel(3y) = 15$

$5x = 9 , color(blue)(x = 9/5$
Substituting $x$ in equation $(1)$ to find $y$
$y = -x + 5$
$y = -9/5 + 5 = (-9+25)/5 , color(blue)(y = 16/5$

The solution for the system of equations is $color(blue)( x= 9/5 and y = 16/5$

How do you solve the system using elimination y = -x + 5y=−x+5y = -x + 5 and 2x - 3y = -62x−3y=−62x - 3y = -6?