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

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

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Answer 1 · 2015-09-22T22:53:52

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

1 Answer

Explanation:

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