Question

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

Answer 1

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

`6x-y=220`

Add `y` to both sides to get:

`6x=y+220`

Subtract `220` from both sides to get:

`y = 6x-220`

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

`13.4 = 0.24x+0.19(6x-220)`

`= 0.24x+(0.19xx6x)-(0.19xx220)`

`= 0.24x+1.14x-41.8`

`= (0.24+1.14)x-41.8`

`= 1.38x-41.8`

Add `41.8` to both sides to get:

`1.38x = 13.4+41.8 = 55.2`

Divide both sides by `1.38` to get:

`x = 55.2/1.38 = 40`

Then from an earlier equation we have:

`y = 6x-220 = (6xx40)-220 = 240-220 = 20`