If the system of equations
4x−3y=2a,2x+y=3a,
has a solution (x,y) when x=3,, compute a.
+23254 4x - 3y = 2a ---> multiply by 3 ---> 12x - 9y = 6a
2x + y = 3a ---> multiply by -2 ---> -4x - 2y = -6a
Add down the columns: 8x - 11y = 0 ---> 11y = 8x ---> y = (8/11)·x
Since x = 3: y = (8/11)·x ---> y = (8/11)·3 ---> y = 24/11
x = 3 and y = 24/11 ---> 4x - 3y = 2a ---> 4(3) - 3(24/11) = 60/11 = 2a ---> a = 30/11
