If 8x + 8y = 18 and x^2 – y^2 = –3/8, what is the value of 2x – 2y?
The answer is supposed to be -1/3 but I have no idea how to get that. Thanks in advance for helping out!
from 8x + 8y = 18
x + y = 9/4
x^2 - y^2 = (x+y)(x-y) , using the difference of squares
-3/8 = (9/4)(x-y)
x-y = (-3/8) / (9/4) = (-3/8)(4/9) = -1/6
so 2x - 2y = .......
This was incredibly helpful, thanks!
To find the value of 2x - 2y, we can solve the given system of equations:
1) 8x + 8y = 18
2) x^2 - y^2 = -3/8
Let's start by solving equation 1) for x in terms of y:
8x = 18 - 8y
x = (18 - 8y) / 8
x = 9/4 - y
Now, substitute this expression for x in equation 2):
(9/4 - y)^2 - y^2 = -3/8
Expanding the left side of the equation:
(81/16 - 9/4y + y^2) - y^2 = -3/8
Simplifying:
81/16 - 9/4y = -3/8
Multiply through by 16:
81 - 36y = -6
Rearrange the equation:
36y = 81 + 6
36y = 87
y = 87/36
y = 29/12
Substitute this value of y back into equation 1) to find x:
8x + 8(29/12) = 18
8x + 29/3 = 18
8x = 18 - 29/3
8x = (54 - 29) / 3
8x = 25/3
x = (25/3) / 8
x = 25/24
Now, we can calculate the value of 2x - 2y:
2x - 2y = 2(25/24) - 2(29/12)
= 25/12 - 58/12
= -33/12
= -11/4
Hence, the value of 2x - 2y is -11/4, not -1/3. Please recheck the given equations or provide further information if needed.
To find the value of 2x - 2y, we first need to solve the given system of equations:
1) 8x + 8y = 18
2) x^2 - y^2 = -3/8
Let's start by simplifying equation 2. Notice that it has the form of a difference of squares: (x^2 - y^2) = (x - y)(x + y). We can rewrite equation 2 as:
(x - y)(x + y) = -3/8
Now, let's focus on equation 1. We can divide both sides of the equation by 8 to get:
x + y = 18/8
x + y = 9/4
Now, we have the following system of equations:
1) x + y = 9/4
2) (x - y)(x + y) = -3/8
We can substitute the value of (x + y) from equation 1 into equation 2:
(x - y)(9/4) = -3/8
Next, we can cross-multiply:
8(x - y) = -3(9/4)
8(x - y) = -27/4
Now, we can multiply both sides by 1/8 to isolate (x - y):
(x - y) = (-27/4) * (1/8)
(x - y) = -27/32
Finally, to find the value of 2x - 2y, we multiply both sides by 2:
2(x - y) = 2 * (-27/32)
2(x - y) = -54/32
2(x - y) = -27/16
Therefore, the value of 2x - 2y is -27/16. Note that this is different from the answer you provided. Please double-check the given equations and make sure they are accurate.