If 7p + 5q = 2 and 8p - 9q = 17, then what is -p + 14q?

1 Answer
Gió
Sep 22, 2015

I found #-15#

Explanation:

Consider first your two initial equations forming a System:
#{(7p+5q=2),(8p-9q=17):}#
Let us solve this system to find #p# and #q#: to solve it let us multiply the first equation by #9#, the second by #5# and add them together in columns:
#{(color(red)(9xx)7p+5q=2),(color(red)(5xx)8p-9q=17):}#

#{(63p+45q=18),(40p-45q=85):}# add them:
#103p+0=103#
so: #p=103/103=1#
substituting into the first equation we get:
#7+5q=2#
#q=-1#

Using these values of #p# and #q# into: #-p+14q# you get:
#-1-14=-15#

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