A.3n+4+3n+4+4n
=3n+3n+4n+4+4
=10n+8
B.11n+4+n-12
=11n+n+4-12
=12n-8
C.6(6n-2)
=36n-12
D.4(3n-2)
=12n-8
E.4n+22-12+8n
=4n+8n+22-12
=12n+10
so,B and D are the expressions that are equivalent to 12n-8.
Answer:
You can use Gaussian Elimination.
Double both sides of the first equation and add the second equation.
6x + 4y = 8
5x - 4y = 3
---------------
11x = 11
x = 1
5 - 4y = 3
-4y = -2
y = 1/2
Step-by-step explanation:
4n = 3m - 1
4n = 3m - 1
Subtract 3m from both sides.
-3m + 4n = -1
Subtract 4n from both sides.
-3m = -4n - 1
Divide both sides by -3.
m = 4/3n + 1/3
m = 4/3n + 1/3
<h3>
Answer: x = 7 and y = 3</h3>
=====================================================
Explanation:
Apply the difference of squares rule
x² - 4y² = 13
x² - (2y)² = 13
(x - 2y)(x + 2y) = 13
Since x and y are positive integers, this means x-2y and x+2y are both integers as well.
The value 13 is prime. Its only factors are 1 and 13
Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:
- A) x-2y = 1 and x+2y = 13
- B) x-2y = 13 and x+2y = 1
----------------
Let's consider case A
We have this system of equations

Add the equations straight down
- x+x becomes 2x
- -2y+2y becomes 0y = 0 which goes away
- 1+13 becomes 14
Therefore we have 2x = 14 solve to x = 7
From here, plug this into either equation to solve for y
x-2y = 1
7 - 2y = 1
-2y = 1-7
-2y = -6
y = -6/(-2)
y = 3
You should get the same result if you used x+2y = 13
----------------
Since we've found that x = 7 and y = 3, notice how case B is not possible
Example: x-2y = 13 becomes 7-2(3) = 13 which is false.
Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.
-----------------
Let's check those x and y values in the original equation
x² - 4y² = 13
7² - 4*(3)² = 13
49 - 4(9) = 13
49 - 36 = 13
13 = 13
The answer is confirmed.
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