if a system has an infinite answer of solutions,use set builder notation to write the solution. if a system has no solution state this.
4p*2q=16
5p+7q=1

Question

if a system has an infinite answer of solutions,use set builder notation to write the solution. if a system has no solution state this. 
4p*2q=16
5p+7q=1

anonymous · Answer

Did you mean 4p+2q=16?

anonymous · Answer

$$4p+2q=16\2p+q=8\\ \5p+7q=1$$If we multiply $2p+q=8$ by $-7$, we get $-14p-7q=-56$. Combine that with our second equation, $5p+7q=1$, and we eliminate the dependency on $q$ to yield:$$-9p=-55\p=\frac{55}9$$Now, we can substitute into our earlier equation, $2p+q=8$, to solve for $q$.$$\frac{110}9+q=8=\frac{72}9\q=\frac{72-110}9=-\frac{38}{9}$$Thus our solutions $(p,q)\in\{(\frac{55}9,-\frac{38}9)\}$