Question

What is the algebraic expression for the sum of two consecutives even numbers

Answer 1

since even numbers differ by 2, you could try x and x+2
But that also works for odd numbers. (e.g., 3,5)

So, since all even numbers are multiples of 2, you should have tried
2k and 2k+2

Answer 2

any even number can be represented by
2n, where n ∊ N, N being the set of natural numbers.
so the next consecutive even number would be 2n+2

sum of two consecutive even numbers = 2n + 2n+2 = 4n+2
= 2(2n + 1)

Answer 3

nice clarification, Reiny, though I'd have said that n∊Z, the integers, since even numbers can be negative.

Answer 4

Transform each equation into standard form (on paper) and then type in the A, B, and C values.
**Remember: A must be a whole number; B and C must be integers.

Equation to Transform A (coefficient for x) B (coefficient for y) C (constant term)
y - 3 = 2(x + 1)
y = 4x - 3
1/3y = 1/2x + 2
y = 3/5(x - 1)
2y - 3x + 10 = 0
2y = -1/4x + 1

Answer 5

Can you help me with this please? ^

Answer 6

what, you can't make your own post?
You want Ax+By = C
So, just start shuffling things around. How hard is that?
The first order of business, if necessary, is to get rid of the fractions. So, let's do
y = 3/5(x - 1)
5y = 3(x-1)
5y = 3x-3
Almost done, you just need to get the 3x onto the left side:
-3x+5y = -3
That does fit the standard form, but I hate leading mus signs, so I'd go with
3x-5y = 3
gotten by multiplying everything by -1.

So, you try the others, and come on back if you get stuck. Not likely, I know.