x=4-y and 4x-2y=-8 substitution method?

For the substitution method, manipulate one of your equations to get a value for one of your variables. Your first equation has this done for you, you have a value for x of 4-y. Use that value for x in the second equation like this:

4x-2y= -8 substitute:
4(4-y)-2y= -8 distribute the 4:
16-4y-2y= -8 combine the like terms -4y and -2y:
16- 6y= -8 subtract 16 from both sides:
-6y= -24 divide by -6
y= 4 note the sign change

Now that you have a number value for y, 4, plug that into one of your equations to solve for x:

x=4-y, y=4
x=4-4
x=0

So now you have x=0, y=4. Because you have a system of equations and you're trying to find the solution to the system, you have to make sure that your solutions solve all the equations in the system, or they aren't a solution to the system. If they don't solve all the equations in your system, then your solution is the empty set. So let's check these values in the other equation:

4x-2y= -8 substitute:
4(0)-2(4)= -8
0-8= -8
-8= -8 check
So the solution to your system is (0,4).

wpf.

2nd equation (value of y):
4(4 - y) - 2y = - 8
16 - 4y - 2y = - 8
6y = 24
y = 4

1st equation (value of x):
= 4 - 4
= 0

Answer: x = 0, y = 4

Checking (1st equation):
0 = 4 - 4
0 = 0

Checking (2nd equation):
4(0) - 2(4) = - 8
0 - 8 = - 8
- 8 = - 8

x=4-y
4x-2y=-8


SO....

4(4-y) - 2y=-8

16-4y-2y=-8
16-6y=-8
24=6y
y=4

then...

x=4-4
x=0


x=0 and y=4

(0,4)

4(4 - y) - 2y = - 8
16 - 6y = - 8
6y = 24
y = 4

x = 0

x = 0 , y = 4

Because you are given an X= problem PLUG IT IN... as my teacher would always say

So you can take the fist equation
x=4-y and place it into the second equation

so it looks like

4(4-y)-2y=-8
which then you simplify to get a number

a y = #

then you place that number into the first equation so that it looks like

x= 4 - #


and there are you Numbers for x and y

x = 4 - y
4x - 2y = -8

4x - 2y = -8
4(4 - y) - 2y = -8
16 - 4y - 2y = -8
-4y - 2y = -8 - 16
-6y = -24
y = -24/-6
y = 4

x = 4 - y
x = 4 - 4
x = 0

∴ x = 0 , y = 4

you know what the variable x equals so substitute it into the second equation:

4(4-y)-2y=-8 Then you want to distribute
16-4y-2y=-8 Then you want to combine like terms
16-6y=-8 Bring the 16 over
-6y=-24 Divide by -6
y= 3