2)
let's say the number is "a".
"two more than the number" ----> a + 2
"five times more than that" -----> 5 * (a + 2) ---> 5(a + 2)
"the sum of that number and 5 times the number more than 2"
a + 5(a + 2)
"is 26 more than four times the number" ----> = 4*a + 26 ---> = 4a + 26
a + 5(a + 2) = 4a + 26
![\bf a+5(a+2)=4a+26\implies a+5a+10=4a+26 \\\\\\ 6a-4a=26-10\implies 2a=16\implies a=\cfrac{16}{2}\implies \boxed{a=8}](https://tex.z-dn.net/?f=%5Cbf%20a%2B5%28a%2B2%29%3D4a%2B26%5Cimplies%20a%2B5a%2B10%3D4a%2B26%0A%5C%5C%5C%5C%5C%5C%0A6a-4a%3D26-10%5Cimplies%202a%3D16%5Cimplies%20a%3D%5Ccfrac%7B16%7D%7B2%7D%5Cimplies%20%5Cboxed%7Ba%3D8%7D)
3)
"eight times the number" ---> 8 * a, or 8a
"3 less than that" ----> 8a - 3
"the number increased by 1" ---> a + 1
"16 times that" ---> 16(a + 1)
"half that" ----> [ 16(a + 1) ] / 2
![\bf 8a-3=\cfrac{16(a+1)}{2}\implies 2(8a-3)=16(a+1) \\\\\\ 16a-6=16a+16\implies \underline{16a-16a}-6=16\implies \stackrel{\textit{inconsistent system}}{-6\ne 16}](https://tex.z-dn.net/?f=%5Cbf%208a-3%3D%5Ccfrac%7B16%28a%2B1%29%7D%7B2%7D%5Cimplies%202%288a-3%29%3D16%28a%2B1%29%0A%5C%5C%5C%5C%5C%5C%0A16a-6%3D16a%2B16%5Cimplies%20%5Cunderline%7B16a-16a%7D-6%3D16%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Binconsistent%20system%7D%7D%7B-6%5Cne%2016%7D)
4)
![\bf \begin{cases} y=5x+1\\ y-2x-1 \end{cases}\qquad 5x+1=2x-1\implies 5x-2x=-1-1 \\\\\\ 3x=-2\implies x=-\cfrac{2}{3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ay%3D5x%2B1%5C%5C%0Ay-2x-1%0A%5Cend%7Bcases%7D%5Cqquad%205x%2B1%3D2x-1%5Cimplies%205x-2x%3D-1-1%0A%5C%5C%5C%5C%5C%5C%0A3x%3D-2%5Cimplies%20x%3D-%5Ccfrac%7B2%7D%7B3%7D)
5)
notice each equation, they're both in slope-intercept form, y = mx + b.
now, notice their slope, is the same for both, notice their y-intercept, it varies.
same slope, different y-intercept simply means, the lines are parallel.