How do you solve the system 0.06x - 0.01y = 2.2 and  0.24x + 0.19y = 13.4 by substitution?

May 22, 2015

First multiply both sides of the first equation by $100$ to get:

$6 x - y = 220$

Add $y$ to both sides to get:

$6 x = y + 220$

Subtract $220$ from both sides to get:

$y = 6 x - 220$

Substitute this express for $y$ into the second equation:

$13.4 = 0.24 x + 0.19 \left(6 x - 220\right)$

$= 0.24 x + \left(0.19 \times 6 x\right) - \left(0.19 \times 220\right)$

$= 0.24 x + 1.14 x - 41.8$

$= \left(0.24 + 1.14\right) x - 41.8$

$= 1.38 x - 41.8$

Add $41.8$ to both sides to get:

$1.38 x = 13.4 + 41.8 = 55.2$

Divide both sides by $1.38$ to get:

$x = \frac{55.2}{1.38} = 40$

Then from an earlier equation we have:

$y = 6 x - 220 = \left(6 \times 40\right) - 220 = 240 - 220 = 20$