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How do you solve by substitution $0.3 x - 0.2 y = 0.5$ $0.3x-0.2y=0.5$ and $x - 2 y = - 5$ $x-2y= -5$ ?

1 Answer

Jun 15, 2015

By simplifying and re-arranging the terms, we get
$(x, y) = (5, 5)$ $(x,y) = (5,5)$

Explanation:

[1] $XXXX$ $color(white)("XXXX")$ $0.3 x - 0.2 y = 0.5$ $0.3x-0.2y=0.5$
[2] $XXXX$ $color(white)("XXXX")$ $x - 2 y = - 5$ $x-2y = -5$

I would suggest the first thing to do is to simplify [1] by multiplying everything by 10
[3] $XXXX$ $color(white)("XXXX")$ $3 x - 2 y = 5$ $3x-2y =5$

In order to use substitution, re-arrange [2] to isolate $x$ $x$
[3] $XXXX$ $color(white)("XXXX")$ $x = 2 y - 5$ $x = 2y-5$

Substitute $2 y - 5$ $2y-5$ for $x$ $x$ in [3]
[4] $XXXX$ $color(white)("XXXX")$ $3 (2 y - 5) - 2 y = 5$ $3(2y-5) -2y = 5$
Simplify
[5] $XXXX$ $color(white)("XXXX")$ $4 y - 15 = 5$ $4y -15 = 5$
[6] $XXXX$ $color(white)("XXXX")$ $y = 5$ $y = 5$

Using [6], substitute $5$ $5$ for $y$ $y$ in [2]
[7] $XXXX$ $color(white)("XXXX")$ $x - 2 (5) = - 5$ $x-2(5) = -5$
[8] $XXXX$ $color(white)("XXXX")$ $x = 5$ $x=5$

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