Solve the following system of equations and find the union of the solutions: $2x+3y=6$ and $5x-y=10$

Step 1 ：First, isolate y in both equations. For the first equation, we get $y=\frac{6-2x}{3}=2-\frac{2x}{3}$. For the second equation, we get $y=5x-10$

Step 2 ：Then, set these two expressions for y equal to each other and solve for x: $2-\frac{2x}{3}=5x-10$. This simplifies to $\frac{5x+2x}{3}=12$, then $x=\frac{12\ast 3}{7}=\frac{36}{7}$

Step 3 ：Substitute $x=\frac{36}{7}$ into the first equation, we get $2\ast \frac{36}{7}+3y=6$, then solve for y, we get $y=\frac{6-2\ast \frac{36}{7}}{3}=\frac{6\ast 7-2\ast 36}{21}=-\frac{18}{21}=-\frac{6}{7}$

Step 4 ：So the solutions to the system of equations are $x=\frac{36}{7}$, $y=-\frac{6}{7}$

Step 5 ：The union of the solutions is the set of all solutions. Since there is only one solution to this system of equations, the union is simply the set $\{\frac{36}{7},-\frac{6}{7}\}$