Question

How do you solve this system for m and b: `342=23m+b, 147=10m +b`?

Answer 1

`(m,b)=(15,-3)`

Explanation:

Given
[1]`color(white)("XXX")342=23m+b`
[2]`color(white)("XXX")147=10m+b`

Subtracting [2] from [1]
[3]`color(white)("XXX")195=13m`

Dividing both sides by `13`
[4]`color(white)("XXX")15=mcolor(white)("XXX")`or equivalently: `m=15`

Substituting `15` for `m` in one of the given equations (I will use [2])
[5]`color(white)("XXX")147=10 * (15)+b = 150 +b`

Subtracting `150` from both sides
[6]`color(white)("XXX")-3=bcolor(white)("XXX")` or equivalently: `b=-3`