SOLUTION: I would greatly appreciate a clear solution with work for this problem: Solve this system of linear equation using any algebraic method.Show solution check. 8x-6y=12

 8x - 6y = 12.   (1)
12x - 9y = 18    (2).


First, simplify the system. Divide the first equation by 2 (both sides). 
Divide the second equation by 3 (both sides). You will get

4x - 3y = 6,     (1')
4x - 3y = 6.     (2').

Now you see that the equations (1') and (2') have identical left sides and identical right sides.
Hence, the system has infinitely many solutions.

To get these solutions, simply express "y" via "x" from either equation:

y = .

For any (arbitrary) value of x you will have the solution of the system y.