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

1 Answer

Apr 16, 2018

$x = 1 and y = 4$ $x=1 and y=4$

Explanation:

Note that the two $x$ $x$ -terms are additive inverses, so if you add the two equations, the $x$ $x$ -terms will be eliminated:

$" "color(blue)(-x)+y = 3" "....... A$
$" "color(blue)(+x)+y = 5" "......."B$

$A+B:" "2y =8$
$color(white)(xxxxx.xxx) y=4$

Substitute $y=4$ into equation $B$ to get $x=1$

Checking in both equations gives:

$-1+4=3$
$+1+4=5$

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