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

1 Answer
Alan P.
Oct 31, 2016

#(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#

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