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How do you find the point of intersection for $3 x - y = 1$ $3x-y=1$ and $x + y = 3$ $x+y=3$ ?

1 Answer

Jul 31, 2015

$(x, y) = (1, 2)$ $(x,y) = (1,2)$

Explanation:

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

Add [1] and [2]
[3] $XXXX$ $color(white)("XXXX")$ $4 x = 4$ $4x = 4$

Divide both sides of [3] by 4
[4] $XXXX$ $color(white)("XXXX")$ $x = 1$ $x = 1$

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

Subtract $1$ $1$ from both sides of [5]
[6] $XXXX$ $color(white)("XXXX")$ $y = 2$ $y = 2$

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