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How do you solve by substitution $x - y \pm 15$ $x-y+-15$ and $x + y = - 5$ $x+y=-5$ ?

1 Answer

Jun 5, 2015

Assuming the first component should have ( $= -$ $=-$ ) instead of ( $\pm$ $+-$ )

[1] $XXXX$ $color(white)("XXXX")$ $x - y = - 15$ $x-y = -15$
[2] $XXXX$ $color(white)("XXXX")$ $x + y = - 5$ $x+y=-5$

Rearranging the terms of [1]
[3] $XXXX$ $color(white)("XXXX")$ $x = y - 15$ $x= y-15$

Substituting $(y - 15)$ $(y-15)$ for $x$ $x$ into [2]
[4] $XXXX$ $color(white)("XXXX")$ $(y - 15) + y = - 5$ $(y-15) + y = -5$
[5] $XXXX$ $color(white)("XXXX")$ $y = 5$ $y=5$

Substituting $5$ $5$ for $y$ $y$ back in [1]
[6] $XXXX$ $color(white)("XXXX")$ $x - 5 = - 15$ $x - 5 = -15$
[7] $XXXX$ $color(white)("XXXX")$ $x = - 10$ $x = -10$

Solution: $(x, y) = (- 10, 5)$ $(x,y) = (-10,5)$

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