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

Oct 31, 2016

$\left(m , b\right) = \left(15 , - 3\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 342 = 23 m + b$
[2]$\textcolor{w h i t e}{\text{XXX}} 147 = 10 m + b$

Subtracting [2] from [1]
[3]$\textcolor{w h i t e}{\text{XXX}} 195 = 13 m$

Dividing both sides by $13$
[4]$\textcolor{w h i t e}{\text{XXX")15=mcolor(white)("XXX}}$or equivalently: $m = 15$

Substituting $15$ for $m$ in one of the given equations (I will use [2])
[5]$\textcolor{w h i t e}{\text{XXX}} 147 = 10 \cdot \left(15\right) + b = 150 + b$

Subtracting $150$ from both sides
[6]$\textcolor{w h i t e}{\text{XXX")-3=bcolor(white)("XXX}}$ or equivalently: $b = - 3$