The given system of equations is expressed as
5x - 2y = 14
6x - 3y = 15
We would apply the method of elimination. We would make the coefficient of y to be equal in both equations by multiplying the first equation by 3 and the second equation by 2. It becomes
15x - 6y = 42
12x - 6y = 30
If we subtract the fourth equation from the third equation, it becomes
15x - 12x - 6y - - 6y = 42 - 30
3x - 6y + 6y = 12
3x = 12
x = 12/3
x = 4
Substituting x = 4 into the first equation, it becomes
5 * 4 - 2y = 14
20 - 2y = 14
2y = 20 - 14
2y = 6
y = 6/2
y = 3
To know if we are correct, we would substitute x = 4 and y = 3 into any of the equations. Substituting into the second equation, it becomes
6 * 4 - 3 * 3 = 15
24 - 9 = 15
15 = 15
This is correct