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

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

Let's solve it using the elimination method:

1. Multiply the first equation by 4 and the second equation by 3 to make the coefficients of x in both equations the same:

Equation 1: \(12x - 7y = 2\) ...multiply by 4: \(48x - 28y = 8\)

Equation 2: \(4x - 5y = 6\) ...multiply by 3: \(12x - 15y = 18\)

2. Now, subtract the second equation from the first equation to eliminate the x term:

\((48x - 28y) - (12x - 15y) = 8 - 18\) \(36x - 13y = -10\)

3. Now, we have a new equation:

\(36x - 13y = -10\)

4. Now, we can solve for y in terms of x:

\(13y = 36x + 10\) \(y = \frac{36x + 10}{13}\)

5. Substitute this value of y back into one of the original equations, let's use the first one:

\(12x - 7(\frac{36x + 10}{13}) = 2\)

Solve for x first and then substitute the value of x back to find y.