7X plus 5Y equals 19 negative 7X minus 2Y equals -17. What is the solution to the system?

1 answer

To solve the system of equations,
7X+5Y=19
7X2Y=17
We can add the two equations together to eliminate the $X$ terms:
3Y=2Y=23
Substituting this value back into the first equation, we have
7X+5(23)=19
7X+103=19
7X=473=1419X=14163=4721

Thus, the solution is $\boxed{(X,Y) = \left(\frac{47}{21}, \frac{2}{3}\right)}$.