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

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

First, we can multiply the first equation by 5 and the second equation by 7 to make the coefficients of y the same:

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

This simplifies to:

60x - 35y = 10 28x - 35y = 42

Now, let's subtract the second equation from the first equation:

60x - 35y - 28x + 35y = 10 - 42 32x = -32 x = -1

Now, substitute x = -1 back into one of the original equations to solve for y. Let's use the first equation:

12(-1) - 7y = 2 -12 - 7y = 2 -7y = 14 y = -2

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