CPhill

Try 5  and note that     3x + y  = -2  ⇒   y  = -2- 3x

Yes you can...you're close  !!!

Good try  !!!...  you have the right idea..just a small error

Let's take it from  here....

4x+3(7-7x)=21

4x + 21 - 21x  =  21     subtract  21  from both sides

4x  - 21x   =0

-17x  = 0   ⇒    x  = 0

Sub this back into y  = 7 - 7x  →  y  = 7 - 7 (0)    = 7  - 0   = 7

(x,y)  =(0,7) ...check this solution in both equations to see that this is true....!!!!

|x - 4| + |x + 4| <= 10

We have these  equations

x - 4  + x + 4   <=  10

2x  <=  10

 x  <= 5

And 

x - 4  + x + 4   >=  -10

2x   >= -10

x >= -5

So.....the solution  is   [-5 , 5  ]

Here's the graph of the solution  :  https://www.desmos.com/calculator/7ar4jqmtg3

Yep... D  too   1/16  = .0625

You're not wrong...but  the there is an easier way without resorting to  those nasty  fractions

6)

x + 4y  = --6

8x  - 2y = -14

Do you see that we have a  single  variable in the first equation ???...in this case, x

So   subtract  4y  from  both  sides  and we get   x   = -6  - 4y

Now..in the second equatiion....just substitute this  for x  and we have

8 [ -6 - 4y ] - 2y  = -14    simplify

-48 - 32y - 2y  =  -14

-48  - 34y  = -14     add 48 to both sides

-34y = 34   divide both sides by  -34

y = -1

The beauty here is that  we already have an expression for x...we just need to fill in the y value

x = -6 - 4(-1)   =    -6 + 4   =  -2

So  (x, y)  = (  -2, -1)

As a hint on number 7...note that  7x  + y  = 7  can be transformed into   y = 7 - 7x

Can you take it from here???...post your work if you get stuck...I'll see if I can "un-stick" you  !!...LOL!!!!

Try 6......post your answer....even if it's incorrect....we can  still fix that  !!!

Yep. after some manipulation as Tertre has done...... each problem wil have a variable already defined  in one of the equations...just substitute the value for that variable into the other equation ....you will  then have a variable in one equation that is easy to solve

BTW...thanks Tertre  !!!!

Correct....RP!!!.....[ and there was nothing to  eliminate] ....LOL!!!!

As in the last one...get the powers on 10 the same.......

.176 x 10^18   =   17.6  x 10^16  = A

22.13  x 10^16   =  B

B - A   =   [22.13  - 17.6 ] x 10 ^16   =   4.53  x 10^16 km