Answer:
To solve the system of equations with elimination, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate y by multiplying the first equation by -1 and then adding it to the second equation. This gives us:
-1(x - 2y) = -1(4)
3x + y = 6
2x - 5y = 2
Now we can solve for x by dividing both sides by 2:
x - 5y/2 = 1
x = 1 + 5y/2
To find the value of y, we can substitute this expression for x into either of the original equations. Let's use the first one:
x - 2y = 4
(1 + 5y/2) - 2y = 4
Simplifying and rearranging, we get:
-4y + 5y = 8 - 2
y = 6
Now we can plug this value of y into the expression for x and get:
x = 1 + 5(6)/2
x = 16
Therefore, the solution of the system is (16, 6). We can check this by plugging these values into both equations and verifying that they are true.