How do you solve the following system: $3 x - 4 y = - 23, 6 x + 7 y = - 9$ $3x - 4y = -23, 6x + 7y = -9$ ?

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Answer 1 · 2016-05-07T03:13:42

$(- \frac{3}{2}, \frac{37}{8})$ $(-3/2, 37/8)$

$[1] 3 x - 4 y = - 23$ $[1] 3x - 4y = -23$
$[2] 6 x + 7 y = - 9$ $[2] 6x + 7y = -9$

Get the equivalent of either variable from either equation.
For example, get the equivalent of $x$ $x$ from $[1]$ $[1]$

$3 x - 4 y = - 23$ $3x - 4y = -23$
$\Rightarrow 3 x = 4 y - 23$ $=> 3x = 4y -23$
$\Rightarrow x = \frac{4 y - 23}{3}$ $=> x = (4y - 23)/3$

Substitute the obtained equivalent of the desired variable into the other equation.

$6 x + 7 y = - 9$ $6x + 7y = -9$

$\Rightarrow 6 (\frac{4 y - 23}{3}) + 7 y = - 9$ $=> 6((4y - 23)/3) + 7y = -9$

$\Rightarrow 2 (4 y - 23) = - 9$ $=> 2(4y - 23) = -9$

$\Rightarrow 8 y - 46 = - 9$ $=> 8y - 46 = -9$

$\Rightarrow 8 y = 37$ $=> 8y = 37$

$\Rightarrow y = \frac{37}{8}$ $=> y = 37/8$

Solve for the other variable now that we know the value of one variable

$3 x - 4 y = - 23$ $3x - 4y = -23$

$\Rightarrow 3 x - 4 (\frac{37}{8}) = - 23$ $=> 3x - 4(37/8) = -23$

$\Rightarrow 3 x - \frac{37}{2} = - 23$ $=> 3x - 37/2 = -23$

$\Rightarrow 6 x - 37 = - 46$ $=> 6x - 37 = -46$

$\Rightarrow 6 x = - 9$ $=> 6x = -9$

$\Rightarrow x = - \frac{9}{6} = - \frac{3}{2}$ $=> x = -9/6 = -3/2$

How do you solve the following system: 3x−4y=−23,6x+7y=−93x - 4y = -23, 6x + 7y = -9 ?