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How do you solve $x + 2 y = 4$ $x + 2y = 4$ and $2 x - y = 3$ $2x - y = 3$ using matrices?

1 Answer

Feb 15, 2016

$x = 2 XXXX y = 1$ $x=2color(white)("XXXX")y=1$

Explanation:

$[(color(red)(x),color(blue)(y),,color(brown)(c)),(color(red)(1),color(blue)(2),"|",color(brown)(4)),(color(red)(2),color(blue)(-1),"|",color(brown)(3))]$

Using Cramer's Rule
$x=(|(color(brown)(4),color(blue)(2)),(color(brown)(3),color(blue)(-1))|) /(|(color(red)(1),color(blue)(2)),(color(red)(2),color(blue)(-1))|)=(-4-6)/(-1-4)=(-10)/(-5)=2$

$y=(|(color(red)(1),color(brown)(4)),(color(red)(2),color(brown)(3))|) /(|(color(red)(1),color(blue)(2)),(color(red)(2),color(blue)(-1))|)=(3-8)/(-1-4)=(-5)/(-5)=1$

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