How do you solve 1/2(x-y) = 2 and 1/2(x+y)+1 = 0?

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Answer 1 · 2018-04-14T21:08:19

$x=1$ and $y=-3$

Solve like simultaneous equations.

Equation 1: $1/2(x-y) = 2$
Expand the brackets to get $1/2x-1/2y=2$

Equation 2: $1/2(x+y)+1 = 0$
Expand the brackets to get $1/2x+1/2y+1=0$

$1/2x-1/2y=2$

$1/2x+1/2y+1=0$

Add the two equations together to get
$1/2x+1/2x+1/2y-1/2y+1=2$

$x+1=2$
$x=1$

Substitute this value of $x$ into either Equation 1 or 2 and solve for $y$

Equation 2: $1/2(1)+1/2y+1=0$
$1/2+1/2y+1=0$
$1/2y+1=-1/2$
$1/2y=-1$ $1/2$
$y = -3$