guys this elimination substitution method stuff really doesnt make sence?

Question

for an equation like this. I already know the answer but have a question

7x-4y=-10
4y=x-2

why do you change the second equation to -x+4y=-2?

I dont get why the x is negative!!! thats all i dont get!

Answer 1

Well, the reason the x is negative is because whenever you move something from one side of an arithmetical equation to the other, you HAVE TO change its sign (since the x was POSITIVE on the RIGHT SIDE of the equals sign, it ends up being NEGATIVE on the LEFT SIDE).

Personally, though, I wouldn't even worry about that... Since the second equation states that 4y=x-2, I would just substitute into the first equation.

Meaning, the first equation is 7x-4y...and since the second equation says 4y=x-2...just replace it in the first equation (meaning it would then be 7x-(x-2)=-10.)

Either way, good luck! I hope this helps!

Answer 2

you get the negitive x because you want to get all your x's on one side so if you subract the x from one side, you do it from the other....so then you have
7x-4y=-10
-x+4y=-2

the -4y and 4y cancel out , thats the elimination part, then you have 6x=12 so x=2 ok?

then you substitute(see where it gets its name?) the 2 instead of x in one of the equations so if you do the first, you get
7(2)-4y=-10 so 14-4y=-10 then you move the 14 over by subtracting so you get -4y=-4 so y=-1

Answer 3

ok by doing that you are doing the elimination method, your goal by making the 2nd one -x+4y=-2 is actually to get the 4y positive, you do this so that you can then add the 2 equations together, to get 6x=-12 then solve for x, then substitute that value back into either equation to solve for y

Answer 4

because you have to do the same thing to both sides of the equation - so when you subtract x from the one side, it needs to be subtracted from the other as well. but since the first side doesn't already have an x there, it becomes negative x because it is like subtracting x from 0
however, it would usually be written as 4y - x = -2

Answer 5

anytime you move a + to the other side of an algebra equation it becomes negative...
for example if i have:
4=3+1 thats the same as 4-3=1 or 4-1=3
all i did was move over the different numbers and switch their signs...so in your example the x is just being moved to the other side of the equal sign

Answer 6

you change the x to a -x because any time you move a variable or a number across the equal sign you have to make it negative. it just the way math works