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 elimination method to solve the system:

Given equations:

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

To eliminate one of the variables, we need to manipulate the equations so that the coefficients of one of the variables are equal in magnitude but opposite in sign.

Let's multiply equation (2) by 3 to make the coefficient of x in both equations equal: 3) 12x - 15y = 18

Now, we have:

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

Subtracting equation (1) from equation (3): (12x - 15y) - (12x - 7y) = 18 - 2 -15y + 7y = 16 -8y = 16 y = -2

Now that we have found the value of y, we can substitute it back into either of the original equations to solve for x. Let's substitute y = -2 into equation (1): 12x - 7(-2) = 2 12x + 14 = 2 12x = -12 x = -1

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