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How do you solve the following linear system: $2x + 3y = 2, x + 6y = 4,$ ?

1 Answer

Jun 22, 2016

$(x,y)=color(green)(""(0,2/3))$

Explanation:

Given:
[1] $color(white)("XXX")2x+3y=2$
[2] $color(white)("XXX")x+6y=4$

[1] $xx 2$
$color(white)("XXX")$ [3] $color(white)("XXX")4x+6y=4$

[3] $-$ [2]
$color(white)("XXX")$ [4] $color(white)("XXX")3x=0$

[4] $div 3$
$color(white)("XXX")$ [5] $color(white)("XXX")x=0$

Substituting (from [5]) $0$ for $x$ in [2]
$color(white)("XXX")$ [6]#color(white)("XXX")0+6y=4

[6] $div 6$
$color(white)("XXX")$ [7] $color(white)("XXX")y=2/3$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For verification purposes, you should check this result by substituting
$x=0$ and $y=2/3$ back into equation [1].

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