12x-7y=2 4x-5y=6

To solve this system of equations, we can use the method of substitution or elimination. Let's use the substitution method:

From the first equation, solve for x in terms of y: 12x - 7y = 2 12x = 7y + 2 x = (7/12)y + 2/12 x = (7/12)y + 1/6

Now substitute this expression for x into the second equation: 4((7/12)y + 1/6) - 5y = 6 (7/3)y + 2/3 - 5y = 6 (7/3 - 5)y + 2/3 = 6 (7/3 - 15/3)y = 18/3 - 2/3 (-8/3)y = 16/3 y = (3/8)(16/3) y = 6

Now substitute y = 6 back into the expression for x: x = (7/12)(6) + 1/6 x = 7/2 + 1/6 x = 21/6 + 1/6 x = 22/6 x = 11/3

Therefore, the solution to the system of equations is: x = 11/3 y = 6