solve each system math help y= -4x y=x+6 and more help?

There are several different methods. I'll do each system using one of the two more popular.

1) I'm afraid I don't know a name for this method (perhaps transitive?).

y= -4x
y=x+6

-4x = y = x + 6
so
-4x = x + 6
-5x = 6
x = -6/5

Now plug this value back into the first equation...
y = -4(-6/5) = 24/5

So your answer is...
(-6/5,24/5)

Check this against the two original equations...


2) I'll use the cancellation method....

x – y = 1
x + y = -7

Add the equations together...
(x - y) + (x + y) = 1 + -7

(Note that the variable y is cancelled out)
2x = -6
x = -3

Now plug this value into the first equation...
-3 - y = 1
-y = 4
y = -4

so (-3,-4) is the answer. Plug these values back into the original equations to verify.

-----------------------------------
3) Here, I'll use the substitution method

6x + 2y = 12
y = 3x

You have the value for y in the second equation, substitute it into the first...
6x + 2(3x) = 12
6x + 6x = 12
12x = 12
x = 1

Now plug this value back into the second equation
y = 3(1)
y = 3

So the answer is
(1,3)

Again, plug the solution into the original equations to verify.

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EDIT

Oops, I missed the first equation in the title.

All better now.

y=-4x
y= x+6

0= 4x +x +6
5x = -6
x= -6/5
-----------------------------------------------------------------------------
x-y = 1
x+y=-7

x= 1+y
1+y +y = -7------------> 2y = -8------------> y = -4
x= 1+(-4)= 1-4 = -3
--------------------------------------------------------------------
(4,-3)------>x-4=0----->y+3=0
(-3,-4)-----> x+3=0 ------> y +4= 0
and so on
-------------------------
6x + 2y = 12
y=3x

6x + 2(3x) = 12------> 6x +6x = 12----> 12x=12---->x=1
y=3x= 3·1 = 3
-----------------
(0,-3)--------> x = 0--------> y+3=0
and so on

1)
y = -4x (solve by using substitution)
y = x + 6

y = -4x
x + 6 = -4x
x + 4x = -6
5x = -6
x = -6/5 (-1.2)

y = -4x
y = -4(-6/5)
y = 24/5 (4.8)

∴ x = -6/5 (-1.2) , 24/5 (4.8)

= = = = = = = =

2)
x - y = 1 (solve by using substitution)
x + y = -7

x - y = 1
x = 1 + y

x + y = -7
(1 + y) + y = -7
y + y = -7 - 1
2y = -8
y = -8/2
y = -4

x - y = 1
x - (-4) = 1
x + 4 = 1
x = 1 - 4
x = -3

∴ x = -3 , y = -4 (-3 , -4)

= = = = = = = =

3)
6x + 2y = 12 (solve by using substitution)
y = 3x

6x + 2y = 12
6x + 2(3x) = 12
6x + 6x = 12
12x = 12
x = 12/12
x = 1

y = 3x
y = 3(1)
y = 3

∴ x = 1 , y = 3 (1 , 3)

2x = -6
x=-3, y = 3 - 7 = -4

6x + 6x = 12
x = 1
y=3