How do you solve the following system?: $x + 2 y = 7, 2 x - 7 y = 1$ $x +2y = 7 , 2x - 7y = 1$

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How do you solve the following system?: $x + 2 y = 7, 2 x - 7 y = 1$ $x +2y = 7 , 2x - 7y = 1$

1 Answer

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Answer 1 · 2018-04-04T16:27:17

$(x, y) = (\frac{51}{11}, \frac{13}{11})$ $(x,y)=(51/11,13/11)$

Explanation:

$x = 7 - 2 y$ $x=7-2y$ solve for $x$ $x$ in terms of $y$ $y$ using the first equation
$2 (7 - 2 y) - 7 y = 1$ $2(7-2y)-7y=1$ plug into the other equation
$14 - 4 y - 7 y = 1$ $14-4y-7y=1$ distribute
$14 - 11 y = 1$ $14-11y=1$ combine
$- 11 y = - 13$ $-11y=-13$
$y = \frac{13}{11}$ $y=13/11$

Now, going back to the other equation (the first one)
$x + 2 (\frac{13}{11}) = 7$ $x+2(13/11)=7$ plug in value of $y$ $y$
$x + \frac{26}{11} = 7$ $x+26/11=7$

$x + \frac{26}{11} = \frac{77}{11}$ $x+26/11=77/11$

$x = \frac{51}{11}$ $x=51/11$

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How do you solve the following system?: $x + 2 y = 7, 2 x - 7 y = 1$ $x +2y = 7 , 2x - 7y = 1$

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Explanation:

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How do you solve the following system?: x+2y=7,2x−7y=1x +2y = 7 , 2x - 7y = 1

1 Answer

Explanation:

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How do you solve the following system?: $x + 2 y = 7, 2 x - 7 y = 1$ $x +2y = 7 , 2x - 7y = 1$