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