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
[tex]\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}[/tex]
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
[tex]\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}[/tex]
4)
[tex]\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}[/tex]
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.
