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How do you find the point of intersection for $x+3y=12$ and $x-y=4$ ?

1 Answer

Jul 1, 2015

The point of intersection occurs at $(x,y) = (6,2)$

Explanation:

[1] $color(white)("XXXX")$ $x+3y=12$
[2] $color(white)("XXXX")$ $x-y = 4$

Subtract [2] from [1] to remove the variable $x$ from the equation
[3] $color(white)("XXXX")$ 4y = 8#

Divide both sides of [3] by $4$
[4] $color(white)("XXXX")$ $y = 2$

Substitute $y=2$ in [1]
[5] $color(white)("XXXX")$ $x+3(2) = 12$

Simplifying
[6] $color(white)("XXXX")$ $x = 6$

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