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How do you solve $2 x + 3 y = 6$ $2x+3y=6$ and $y = 2 x - 6$ $y=2x-6$ using substitution?

1 Answer

May 15, 2016

$(x, y) = (3, 0)$ $(x,y)=color(blue)(""(3,0))$
(see below for solution by substitution)

Explanation:

Given
[1] $XXX 2 x + 3 y = 6$ $color(white)("XXX")2x+3y=6$
[2] $XXX y = 2 x - 6$ $color(white)("XXX")y=2x-6$

Since from [2] we have that $y = 2 x - 6$ $y=2x-6$
we can replace $y$ $y$ with $(2 x - 6)$ $(2x-6)$ in [1]
to get
[3] $XXX 2 x + 3 (2 x - 6) = 6$ $color(white)("XXX")2x+3(2x-6)=6$

Simplifying
[4] $XXX 8 x - 18 = 6$ $color(white)("XXX")8x-18=6$

[5] $XXX \to 8 x = 24$ $color(white)("XXX")rarr 8x=24$

[6] $XXX \to x = 3$ $color(white)("XXX")rarr x=3$

Since from [6] $x = 3$ $x=3$
we can replace $x$ $x$ with $(3)$ $(3)$ in [2]
to get
[7] $XXX y = 2 (3) - 6$ $color(white)("XXX")y=2(3)-6$

and simplifying
[8] $XXX y = 0$ $color(white)("XXX")y=0$

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