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

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

Given equations:

1. 12x - 7y = 2
2. 4x - 5y = 6

To eliminate one of the variables, let's first manipulate the equations to make the coefficients of either x or y the same:

Multiply equation 2 by 3: 3(4x - 5y) = 3(6) 12x - 15y = 18

Now, the equations become:

1. 12x - 7y = 2
2. 12x - 15y = 18

Subtract equation 1 from equation 2: (12x - 15y) - (12x - 7y) = 18 - 2 12x - 15y - 12x + 7y = 16 -8y = 16 y = -2

Now, substitute y = -2 back into equation 1 to solve for x: 12x - 7(-2) = 2 12x + 14 = 2 12x = -12 x = -1

Therefore, the solution to the system of equations is x = -1, y = -2.