Solve by the substitution method.?

Question

Solve by the substitution method.
x - y = -8
x + y = 8

What is the solution of the system?_______
type an ordered pair.

Answer 1

Solve for "x" or, "y" in either equation. Let's solve for "y" in the 2nd equation... x+y = 8

First: subtract "x" from both sides (when you move a term to the opposite side, always use the opposite sign).

x - x + y = 8 - x
y = 8 - x

Sec: replace 8-x with "y" in the 1st equation... x - y = -8

x - (8 - x) = - 8
x - 8 - (-x) = -8
x - 8 + x = - 8
2x - 8 = - 8 > *Add 8 with both sides.
2x - 8 +8 = - 8+8
2x = 0 > Divide both sides by 2.
2x/2 = 0/2
x = 0/2
x = 0

Third: replace "0" with "x" in the 2nd equation... x + y = 8

0 + y = 8
y = 8

Solution (0, 8)

Answer 2

x - y = -8
x + y = 8
First equation => x = y - 8
By substituting the value of x in equation second we get
y - 8 + y = 8
=> 2y - 8 = 8
=> 2y = 8 + 8
=> 2y = 16
=> y = 16/2
=> y = 8
substitute the value of y in second equation
x + 8 = 8
=> x = 8 - 8
=> x = 0
Hence solution of given system as an ordered pair is (0,8)

Answer 3

I disagree with Ben. Solving by substitution DOES NOT mean you make one of the variables 0 and then solved for the other. It means you solve for a variable in one equation and substitute the answer in the second equation to find the values of both variables.

x-y= -8
-y=-8-x or y=8+x
Substitute the answer for "Y" in the second equation.

x+8+x=8
2x+8+8
2x=0
x=0

Now you take x=0 and plug it into the other equation to solve for the numerical value of "Y".

0-y=-8
-y=-8
y=8
Solving it that way gives you the following solution for the variables x and y

x=0
y=8

Answer 4

Solution (x , y) = ( 0, 8 )


STEPS:

x - y = -8.....(1)

x + y = 8..... (2)

From (1), x = y - 8

Substituting this value for x in eqation ( 2 ),

(y - 8 ) + y = + 8

=> 2y - 8 = +8

=> 2y = 8 + 8 = 16.

y = 16 / 2 = +8 ..... (3)

Substituting the value for y in the equation (2),

x + y = +8

=> x+ 8 = +8

=> x = 8 - 8 = 0.... (4)

x = 0; y = 8. Answer

Answer = (x, y) = ( 0,8)

Answer 5

Substitue 4y-2 or 6y+8 into one of the equations, whichever one you choose will be fine because it will be the same equation no matter what, just backwards. I'll try to simplify it more: eq. 1) x=4y-2 eq. 2) x=6y+8 Substitute either 4y-2 or 6y+8 into the other equation. If you use 4y-2 from eq. 1, eq. 2 would now look like this: 4y-2=6y+8 because if x is 4y-2, you can just put it right into where the x is in eq. 2 - because x IS 4y-2. It is the same for if you use 6y+8 from eq. 2 -- x IS 6y+8 so you can put this phrase into equation one where the x is because 6y+8 equals x. It would look like this - 6y+8=4y-2 Then after you have either 6y+8=4y-2 or 4y-2=6y+8, you can solve for y by adding together like terms. Using 4y-2=6y+8...... Add the 4y and 6y together by subtracting 4y from the positive 4y on the left side of the equal sign and by 6y to get 2y on the right side of the equal sign : 4y-2=6y+8 -4y -4y ^ the +4y and -4y cancels out leaving... -2=2y+8 you are trying to get y by itself, so you need to subtract 8 from the positive 8 on the right side and subtract 8 from the negative 2 on the left to get -10 on the left: -2=2y+8 -8 -8 ^ the +8 and - 8 cancels out leaving.... -10=2y To get y by itself, you need to divide the 2y by 2 (do the opposite to cancel the 2 out, like we did when it was addition/subtraction), and divide the -10 by 2: -10=2y -10/2=2y/2 ^the multiplied 2 and divided 2 cancels out leaving.... -5=y <--- -5 IS y ---- So now that you have y, you can put in -5 in either eq.1 or 2 and solve : (using eq 1): x = 4y-2 x = 4(-5)-2 x = -20-2 x = -22 ! So the ordered pair to solve these equations is (x, y) : (-22, -5)

Answer 6

The answer is (0, 8). X is zero Y is 8.

Answer 7

i) x= -8+y
x=8-y
ii)
-8+y=8-y
y+y=8+8
2y=16
y=8
iii)
x-8=-8
x=-8+8
x=0

Answer 8

oh so by elimination and substitution method
x+y=8
x=8-y
8-y-y=-8
-2y=-16
y=8
x=0

Answer 9

y = 8 - x
x - (8 - x) = - 8
2x - 8 = - 8
2x = 0
x = 0
y = 8
(0,8) is solution.

Answer 10

x-y= -8
make x=0
-y=-8
y=8
make y=0
x=-8

x+y=8
make x=0
y=8
make y=0
x=8