Question

Help someone!! Thxxx

Answer 1

has no solution

Explanation:

4p+6q=13

solve for p:

4p=13-6q

p=(13-6q)/4 try q=1

p=13-6/4=1.75

p=13-12/4=1/4

also because they both even

Answer 2

Answer: E. None

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Explanation:

At first glance, you could argue there are infinitely many solutions (since there are infinitely many points on the given line, there is likely infinitely many integer points).

However, let's factor 4p+6q to get 2(2p+3q). Note that 2 is a factor, so the expression 4p+6q is some even integer. This is true for any (p,q) pairing. But the right hand side 13 is odd. This is a contradiction and therefore there are no solutions.

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The closest you can get is (p,q) = (-1,3) since 4p+6q = 4(-1)+6(3) = -4+18 = 14.

Or you could do (5,-1) to get 4p+6q = 4(5)+6(-1)=20-6 = 14

There are infinitely many ways to get close to 13, but we can't land exactly on 13 itself.