Question

How can 1/5x − 2 = 1/3x + 8 be set up as a system of equations? a . 5y − 5x = −10. 3y − 3x = 24 b. 5y − 5x = −10. 3y + 3x = 24 c. 5y + x = −10. 3y + x = 24 d. 5y − x = −10. 3y − x = 24

Answer 1

The answer is d. 5y − x = −10. 3y − x = 24

$\frac{1}{5}x-2= \frac{1}{3}x+8=y$
⇒   $y= \frac{1}{5}x-2$
      $y= \frac{1}{3}x+8$
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$y= \frac{x}{5} -2= \frac{x}{5} - \frac{10}{5} = \frac{x-10}{5}$
$y= \frac{x}{3} +8= \frac{x}{3} + \frac{24}{3} = \frac{x+24}{3}$
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$y= \frac{x-10}{5}$            ⇒     $5y=x-10$
$y= \frac{x+24}{3}$           ⇒     $3y=x+24$
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$5y-x=-10$
$3y-x=24$