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# How do you solve the system c = 3d - 27 and 4d + 10c = 120 by substitution?

May 19, 2015

equations provided are:
$c = 3 d - 27$ .................$\left(1\right)$
$4 d + 10 c = 120$ ..........$\left(2\right)$

Substituting equation $\left(1\right)$ in equation $\left(2\right)$
$4 d + 10 \left(3 d - 27\right) = 120$
$4 d + 30 d - 270 = 120$
$34 d = 390$
$d = \left(\frac{390}{34}\right) \approx 11.5$

Substituting the value of $d$ to find $c$

$c = 3 d - 27 = 3 \times \left(11.5\right) - 27$
$= 34.5 - 27 = 7.5$

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