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

To solve this system of linear equations by elimination, you can multiply both equations by suitable constants to make the coefficients of either x or y the same in both equations. Here's the step-by-step solution:

Given equations:

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

First, let's make the coefficients of y the same in both equations: Multiply equation 1 by 5 and equation 2 by 7: 5*(12x - 7y) = 52 7(4x - 5y) = 7*6

This simplifies to: 60x - 35y = 10 28x - 35y = 42

Now, we will subtract the second equation from the first to eliminate y: 60x - 35y - (28x - 35y) = 10 - 42 32x = -32 x = -32/32 x = -1

Now that we have found the value of x, we can substitute it 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.