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How do you solve the following system: $4 x - 2 y = 4, 4 x - 5 y - 23 = 0$ $4x-2y=4 , 4x-5y-23=0$ ?

1 Answer

Jun 14, 2017

$x = - \frac{13}{6} and y = - \frac{19}{3}$ $x = -13/6 and y = -19/3$

Explanation:

Write both equations with $4 x$ $4x$ as the subject.

$4 x = 2 y + 4 and 4 x = 5 y + 23$ $4x = 2y+4" and "4x = 5y +23$

$\times \times \times \times 4 x = 4 x$ $color(white)(xxxxxxxx)4x = 4x$

$\times \times x 5 y + 23 = 2 y + 4$ $color(white)(xxxxx)5y +23 = 2y+4$

$\times \times x 5 y - 2 y = 4 - 23$ $color(white)(xxxxx)5y -2y = 4-23$

$\times \times \times \times 3 y = - 19$ $color(white)(xxxxxxxx)3y = -19$

$\times \times \times \times x y = - \frac{19}{3}$ $color(white)(xxxxxxxxx)y = -19/3$
$4 x = (2 y + 4)$ $4x= (2y+4)$

$x = \frac{2 y + 4}{4}$ $x = (2y+4)/4$

$x = (2 (\frac{- 19}{3}) + 4) \div 4$ $x = (2((-19)/3) +4)div 4$

$x = - \frac{13}{6}$ $x = -13/6$

Check:

$4 x = 5 y + 23$ $4x = 5y+23$

$4 \times \frac{- 13}{6} = 5 (\frac{- 19}{3}) + 23$ $4xx(-13)/6 = 5((-19)/3)+23$

$- \frac{26}{3} = - \frac{26}{3}$ $-26/3 = -26/3$

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