Question 1207606
Let's solve this system of equations using the elimination method.

First, we can multiply the two equations by necessary multiples such that the coefficients of y's in both equations are the same:

1. Multiply the first equation by 2 and the second equation by 3:

4x + 6y = 24 (Multiplying the first equation by 2)
3x - 6y = -9 (Multiplying the second equation by 3)

1. Add both equations to eliminate y:

(4x + 6y) + (3x - 6y) = 24 + (-9)
4x + 3x = 15
7x = 15

1. Divide by 7:

x = 15/7

1. Substitute the value of x into one of the original equations to find the value of y:

2x + 3y = 12
2(15/7) + 3y = 12

1. Solve for y:

3y = 12 - 30/7
3y = (84 - 30)/7
3y = 54/7
y = 18/7

So, the solution to the system is x = 15/7 and y = 18/7.