How do you solve the following system: $- x + 6 y = 12, 2 x - y = 7$ $-x+6y=12 , 2x-y=7$ ?

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Answer 1 · 2017-03-22T20:22:39

$x = \frac{54}{11}, y = \frac{31}{11}$ $x=54/11, y=31/11$

$2 x - y = 7$ $2x-y=7$
$- x + 6 y = 12 (\cdot 2)$ $-x+6y=12 (*2)$

$2 x - y = 7$ $2x-y=7$
$- 2 x + 12 y = 24$ $-2x+12y=24$

add together:

$(0 +) 11 y = 31$ $(0+)11y=31$
$11 y = 31$ $11y=31$
$y = \frac{31}{11} or 2 \frac{9}{11}$ $y=31/11 or 2 9/11$

$2 x - y = 7$ $2x-y=7$
$2 x - 2 \frac{9}{11} = 7$ $2x - 2 9/11 = 7$

add $2 \frac{9}{11}$ $2 9/11$ :

$2 x = 9 \frac{9}{11} or \frac{108}{11}$ $2x = 9 9/11 or 108/11$

divide by 2:
$x = \frac{54}{11}$ $x = 54/11$

$x = \frac{54}{11}, y = \frac{31}{11}$ $x=54/11, y=31/11$

How do you solve the following system: −x+6y=12,2x−y=7-x+6y=12 , 2x-y=7 ?