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How do you find the point of intersection for $x - y = 4$ $x-y=4$ and $x - 3 y = - 6$ $x-3y= -6$ ?

1 Answer

Jun 28, 2015

$x - y = 4$ $x-y=4$ and $x - 3 y = - 6$ $x-3y=-6$ intersect at $(x, y) = (9, 5)$ $(x,y) = (9,5)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $x - y = 4$ $x-y=4$
[2] $XXXX$ $color(white)("XXXX")$ $x - 3 y = - 6$ $x-3y = -6$

Subtract [2] from [1]
[3] $XXXX$ $color(white)("XXXX")$ $2 y = 10$ $2y = 10$

Divide both sides by 2
[4] $XXXX$ $color(white)("XXXX")$ $y = 5$ $y = 5$

Substitute $5$ $5$ for $y$ $y$ back in [1] (we could have used either [1] or [2])
[5] $XXXX$ $color(white)("XXXX")$ $x - 5 = 4$ $x - 5 = 4$

Add 5 to both sides
[6] $XXXX$ $color(white)("XXXX")$ $x = 9$ $x = 9$

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