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

Answer 1

To solve the system of equations,
\[7X + 5Y = 19\]
\[-7X - 2Y = -17\]
We can add the two equations together to eliminate the $X$ terms:
\[3Y = 2 \Rightarrow Y = \frac{2}{3}\]
Substituting this value back into the first equation, we have
\[7X + 5 \left(\frac{2}{3}\right) = 19\]
\[7X + \frac{10}{3} = 19\]
\[7X = \frac{47}{3} = \frac{141}{9} \Rightarrow X = \frac{141}{63} = \frac{47}{21}\]

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