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How do you solve the simultaneous equations $y = 3x$ and $x + 2y =21$ ?

1 Answer

Jul 13, 2015

Since we are given an expression for $y$ as one of the equations, the simplest way to solve this pair of equations is through substitution.
$(x,y) = (3,9)$

Explanation:

[1] $color(white)("XXXX")$ $y=3x$
[2] $color(white)("XXXX")$ $x+2y = 21$

Based on [1], we can replace $y$ with $3x$ in [2], giving
[3] $color(white)("XXXX")$ $x+2(3x) = 21$
Simplifying:
[4] $color(white)("XXXX")$ $7x = 21$
or
[5] $color(white)("XXXX")$ $x=3$

Based on [5], we can replace $x$ with $3$ in [1], giving
[6] $color(white)("XXXX")$ $y = 3(3)$
or
[7] $color(white)("XXXX")$ $y= 9$

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