To solve for x, add 3 to both sides, multiply both sides by -1, then take the square both sides.
Step 1: Set the two equations equal to each other and solve for x.
3x -5 = 6x - 8
3x + (-5+5) = 6x -8 + 5
(3x - 6x) = (6x - 6x) - 3
-3x/-3 = -3/-3
x = 1
Step 2: To solve for y take one of the given equation of your choice (for the purpose of this explanation I will only do y = 3x - 5) and replace x with 1, then solve for y
y = 3(1) - 5
y = 3 - 5
y = -2
(1,-2)
Check:
-2 = 3(1) - 5 ---> - 2 = -2
-2 = 6(1) - 8 ---> -2 = -2
Hope this helped!
By the binomial theorem,
![(2x+y)^4=\displaystyle\sum_{k=0}^4\binom 4k(2x)^{4-k}y^k=\sum_{k=0}^4\binom 4k2^{4-k}x^{4-k}y^k](https://tex.z-dn.net/?f=%282x%2By%29%5E4%3D%5Cdisplaystyle%5Csum_%7Bk%3D0%7D%5E4%5Cbinom%204k%282x%29%5E%7B4-k%7Dy%5Ek%3D%5Csum_%7Bk%3D0%7D%5E4%5Cbinom%204k2%5E%7B4-k%7Dx%5E%7B4-k%7Dy%5Ek)
where
![\dbinom nk=\dfrac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=%5Cdbinom%20nk%3D%5Cdfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D)
Then the coefficients of the
terms in the expansion are, in order from
to
,
![\dbinom 402^{4-0}=1\cdot2^4=16](https://tex.z-dn.net/?f=%5Cdbinom%20402%5E%7B4-0%7D%3D1%5Ccdot2%5E4%3D16)
![\dbinom412^{4-1}=4\cdot2^3=32](https://tex.z-dn.net/?f=%5Cdbinom412%5E%7B4-1%7D%3D4%5Ccdot2%5E3%3D32)
![\dbinom422^{4-2}=6\cdot2^2=24](https://tex.z-dn.net/?f=%5Cdbinom422%5E%7B4-2%7D%3D6%5Ccdot2%5E2%3D24)
![\dbinom432^{4-3}=4\cdot2^1=8](https://tex.z-dn.net/?f=%5Cdbinom432%5E%7B4-3%7D%3D4%5Ccdot2%5E1%3D8)
![\dbinom442^{4-4}=1\cdot2^0=1](https://tex.z-dn.net/?f=%5Cdbinom442%5E%7B4-4%7D%3D1%5Ccdot2%5E0%3D1)
I haven’t met them but they seem like very nice fun people ...
Have you met them? :)
If we begin with the first term, 2, mult. it by 4 and then subtract 3, we get 5 (not 4, as shown).
If we begin with 4, mult. it by 4 and then subtract 3, we get 13. This agrees with the terms of the given sequence.
If we begin with 13, mult. it by 4 and then subtract 3, we get 49. This agrees with the terms of the given sequence.
Remove the first term, 2, and then the remaining terms follow the given procedure for finding terms.