Question 17873
Wow, long question!
This question seems a little old, but I'll still answer it.
Your question 5 with substitution
{{{x=4y+5}}}
{{{x=3y-2}}}
Don't let the 2 x's confuse you.
All you need to do (because you are using substitution) is move one of the x's over and the number without a variable over to take its spot.
{{{4y-x=-5}}} - New equation
Take the second equation and substitute!
{{{4y-(3y-2)=-5}}}
{{{4y-3y+2=-5}}}
{{{y=-7}}}
Plug -7 back into the original equation to get X
{{{x=4(-7)+5}}}
{{{x=-28+5}}}
{{{x=-23}}}
*CHECK*
Plug (-23,-7) back into your answer to make sure you get the right answer. On homework, I would just check the answer in the book to make sure you got it right, but on tests, I highly reccomend checking.
{{{-23=4(-7)+5}}}
{{{-23=-23}}} CORRECT!

Your question 7 with elimination
{{{3x-5y=16}}}
{{{-3x+2y=-10}}}
Great! You already have coinciding X terms! All you need to do is get rid of it. How? Add 3 to -3 and you get 0!
{{{-3y=6}}}
{{{y=-2}}}
Plug -2 back in the original equation to find X
{{{3x-5(-2)=16}}}
{{{3x+10=16}}}
{{{3x=6}}}
{{{x=2}}}
*CHECK*
{{{3(2)-5(-2)=16}}}
{{{6+10=16}}} CORRECT!

Your 3rd question using elimination
{{{4x+7y=6}}}
{{{6x+5y=20}}}
All you have to do is multiply the X or Y values to make them equal.
For X, you can make them both 24 by multiplying the top by 6 and the bottom by 4
For Y, you can make them both 35 by multiplying the top by 5 and the bottom by 7
I'll make the X values 24 because the number is smaller.
{{{24x+42y=36}}}
{{{24x+20y=80}}}
Subtract
{{{22y=-44}}}
{{{y=-2}}}
Plug -2 for Y to get X
{{{4x+7(-2)=6}}}
{{{4x-14=6}}}
{{{4x=20}}}
{{{x=5}}}
*CHECK*
{{{4(5)+7(-2)=6}}}
{{{20-14=6}}} CORRECT!

Your question 16 (I reccomend elimination)
{{{x+2y=6}}}
{{{3x-2y=2}}}
Add
{{{4x=8}}}
{{{x=2}}}
Plug 2 in for X to get Y
{{{(2)+2y=6}}}
{{{2y=4}}}
{{{y=2}}}
*CHECK*
{{{(2)+2(2)=6}}}
{{{2+4=6}}} CORRECT!

Hope this all helps!