How do you solve $2 x - 7 y = 6$ $2x-7y=6$ , $x + 3 y = 2$ $x+3y=2$ ?

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How do you solve $2 x - 7 y = 6$ $2x-7y=6$ , $x + 3 y = 2$ $x+3y=2$ ?

1 Answer

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Answer 1 · 2018-03-28T20:22:27

$(x, y) = (\frac{32}{13}, - \frac{2}{13})$ $(x,y) = (32/13, -2/13)$

Explanation:

$x = 2 - 3 y$ $x=2-3y$ using the second equation, define x in terms of y
$2 (2 - 3 y) - 7 y = 6$ $2(2-3y)-7y=6$ plug the above into the first equation
$4 - 6 y - 7 y = 6$ $4-6y-7y=6$ distribute
$4 - 13 y = 6$ $4-13y=6$
$13 y = - 2$ $13y=-2$
$y = - \frac{2}{13}$ $y=-2/13$
Going back to the first equation, we can plug this value in for y to achieve x.
$x = 2 - 3 (- \frac{2}{13})$ $x=2-3(-2/13)$
$x = \frac{26}{13} + \frac{6}{13}$ $x=26/13+6/13$

$x = \frac{32}{13}$ $x=32/13$

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How do you solve $2 x - 7 y = 6$ $2x-7y=6$ , $x + 3 y = 2$ $x+3y=2$ ?

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