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How do you solve the system of linear equations $2 x + y = 9$ $2x + y = 9$ and $x - y = 3$ $x - y = 3$ ?

1 Answer

Feb 17, 2016

$(x, y) = (4, 1)$ $(x,y)=(4,1)$

Explanation:

Given:
[1] $XXX 2 x + y = 9$ $color(white)("XXX")2x+y=9$
[2] $XXX x - y = 3$ $color(white)("XXX")x-y=3$

Add equations [1] and [2] to get
[3] $XXX 3 x = 12$ $color(white)("XXX")3x=12$

Divide equation [3] by $3$ $3$
[4] $XXX x = 4$ $color(white)("XXX")x=4$

Substitute $4$ $4$ for $x$ $x$ in [2]
[5] $XXX 4 - y = 3$ $color(white)("XXX")4-y=3$

Think about it for a minute, then write
[6] $XXX y = 1$ $color(white)("XXX")y=1$

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