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

1 Answer

Oct 31, 2016

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

Explanation:

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

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

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

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

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

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