Question 845824
This one was fun. The key to solving this is to simplify first. Let's start off by labeling the different equations as equations 1 and 2

1) 4(x - 2) = 8(y - 1)
2) 16y - 32 = 2x + 4


The first thing you want to do is simplify equation 1 by using the distributive property to simplify both sides of the equation.

So equation 1 looks like this after using the distributive property:

4x-8 = 8y-8 

Now, once we have this simplified we want to simplify it even more. Let's try to get the y alone. We do that by dividing both sides by 8 to get this:

1/2x-8 = y-8 

Now we just add 8 to both sides to get y by itself and we get this:

y = 1/2x. 


So now we can express y in terms of x. Now let's use that knowledge to solve for equation 2


Equation 2 says 
16y - 32 = 2x + 4.


Now all you need to do is substitute what we know y is into the equation and solve for x since we can now express y in terms of x.

16(1/2x) - 32 = 2x + 4. Now, solve for x.


Equation 2 becomes 


8x - 32 = 2x + 4.

Subtract 2x from both sides


6x - 32 = 4 


Add 32 to both sides.


6x = 36

Divide each side by 6.

x = 6


And since we know that y =1/2x that means y = 3. 



Now plug in the values of x and y into the original equations to see of they check out.


4(6-2) = 8(3-1)

4(4) = 8(2)

16 = 16. Everything checks out for equation 1 so let's try equation 2



16(3)-32 = 2(6) + 4

48 - 32 = 12 + 4

16 = 16. Equation 2 checks out so the solution is (6,3).