x=y-8 -x-y=0

Question

x=y-8

-x-y=0

please help and show step by step

Answer 1

The first equation x=y-8 is, subtract y from each side, x-y=-8

the second equation -x-y=0 is, multiply by -1,            x+y=0

Now add and get                                                      2x+0=-8 or 2x=-8 or x=-4

        Use this result in the second equation to get      -4+y=0 or y=4

Or subtract the equations to get                                0-2y=-8 or y=4

Answer 2

Hello James.

 

x=y-8

So the simplest way you can do this is to REPLACE or SUBSTITUTE the "x" in the second equation with "y-8."

In other words, the second equation can be rewritten as:

-(y-8)-y=0 

*it's important to put the parenthesis around the "y-8" as it is the entire value that is being negated. 

Now DISTRIBUTE the negative over the parenthesis and you get -y+8-y=0

Combine the y and you get -2y+8=0

Subtract 8 from both sides and you get -2y=-8

Divide by -2 and you get the answer for y! y=4

Now all you have to do to find the x is to take the first equation and replace the y with the 4. 

So it'll look like this x=4-8

Therefore, x is -4. Or x=-4

 

As a side note, there is a way to solve these together by adding the second equation to the first one as a whole... However, I felt maybe you didn't get to that stage yet and didn't want to confuse you. 

The best thing to remember with these is:

1) Find ONE variable in terms of the second one (which in this case is simply the first equation) 

2) REPLACE or SUBSTITUTE the variable you've found in Step 1 into the second equation. 

3) COMBINE all variables on one side and numbers on the other and solve! 

*be careful with your signs!*

 

Best,

Tae