Multiply both sides of the first equation by 3.
Multiply both sides of the second equation by 2.
6x + 9y = 3
-6x - 4y = -2
Now add them.
5x = 1
x = 1/5
Now plug in 1/5 for x in the first original equation.
2x + 3y = 1
2 * 1/5 + 3y = 1
2/5 + 3y = 1
2 + 15y = 5
15y = 3
y = 1/5
The solution is x = 1/5; y = 1/5.
There is one solution.
