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How do you solve the following system: $- x + 6 y = 12, x - 4 y = 2$ $-x+6y=12, x-4y=2$ ?

1 Answer

Dec 14, 2015

$\times x = 30$ $color(white)(xx)x=30$ , $y = 7$ $y=7$

Explanation:

$\times - x + 6 y = 12, x - 4 y = 2$ $color(white)(xx)-x+6y=12, x-4y=2$

$\times - x + 6 y = 12 \Leftrightarrow y = \frac{x + 12}{6}$ $color(white)(xx)-x+6y=12<=>y=(x+12)/6$
$\times x - 4 y = 2 \Leftrightarrow y = \frac{x - 2}{4}$ $color(white)(xx)x-4y=2<=>y=(x-2)/4$

$\times y = \frac{x + 12}{6}$ $color(white)(xx)y=(x+12)/6$
$\Rightarrow \frac{x - 2}{4} = \frac{x + 12}{6}$ $=>color(blue)((x-2)/4)=(x+12)/6$

Multiply both side by $12$ $color(red)12$ :
$\times 12 \times \frac{x - 2}{4} = 12 \times \frac{x + 12}{6}$ $color(white)(xx)color(red)(12xx)(x-2)/4=color(red)(12xx)(x+12)/6$
$\Rightarrow 3 x - 6 = 2 x + 24$ $=>3x-6=2x+24$

Add $- 2 x + 6$ $color(red)(-2x+6)$ to both side:
$\times 3 x - 6 - 2 x + 6 = 2 x + 24 - 2 x + 6$ $color(white)(xx)3x-6color(red)(-2x+6)=2x+24color(red)(-2x+6)$

$\times x = 30$ $color(white)(xx)x=30$

$\times y = \frac{x - 2}{4}$ $color(white)(xx)y=(x-2)/4$

$\times x = \frac{30 - 2}{4}$ $color(white)(xxx)=(color(red)30-2)/4$
$\times x = \frac{28}{4}$ $color(white)(xxx)=(color(red)28)/4$
$\times x = 7$ $color(white)(xxx)=7$

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