Question

Please help me, I really would appreciate it. I am struggling with this.

Answer 1

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

$\bf a+5(a+2)=4a+26\implies a+5a+10=4a+26 \\\\\\ 6a-4a=26-10\implies 2a=16\implies a=\cfrac{16}{2}\implies \boxed{a=8}$

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

$\bf 8a-3=\cfrac{16(a+1)}{2}\implies 2(8a-3)=16(a+1) \\\\\\ 16a-6=16a+16\implies \underline{16a-16a}-6=16\implies \stackrel{\textit{inconsistent system}}{-6\ne 16}$

4)

$\bf \begin{cases} y=5x+1\\ y-2x-1 \end{cases}\qquad 5x+1=2x-1\implies 5x-2x=-1-1 \\\\\\ 3x=-2\implies x=-\cfrac{2}{3}$

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.