keeping in mind that

x = percent rate for the 17000 investment.
y = percent rate for the 11000 investment.
so the amount for the 17000 interest will just be (x/100) * 17000, or namely 170x.
and the amount of interest earned for the 11000 is (y/100) * 11000, or just 110y.
now, regardless of what "x" and "y" are, we know that the interest from the 17000 is higher by 308 bucks, therefore 170x = 110y + 308.
we also know that the rate of <u>x</u> is higher as well than <u>y</u> by 0.4%, so then x = y + 0.4.
![\bf \begin{cases} 170x=110y+308\\ \boxed{x}= y +0.4\\[-0.5em] \hrulefill\\ 170\left( \boxed{y+0.4} \right)=110y+308 \end{cases} \\\\\\ 170y+68=110y+308\implies 60y=240\implies y=\cfrac{240}{60}\implies \blacktriangleright y=\stackrel{\%}{4} \blacktriangleleft \\\\\\ x=y+0.4\implies \blacktriangleright x=\stackrel{\%}{4.4} \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20170x%3D110y%2B308%5C%5C%20%5Cboxed%7Bx%7D%3D%20y%20%2B0.4%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20170%5Cleft%28%20%5Cboxed%7By%2B0.4%7D%20%5Cright%29%3D110y%2B308%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5C%5C%20170y%2B68%3D110y%2B308%5Cimplies%2060y%3D240%5Cimplies%20y%3D%5Ccfrac%7B240%7D%7B60%7D%5Cimplies%20%5Cblacktriangleright%20y%3D%5Cstackrel%7B%5C%25%7D%7B4%7D%20%5Cblacktriangleleft%20%5C%5C%5C%5C%5C%5C%20x%3Dy%2B0.4%5Cimplies%20%5Cblacktriangleright%20x%3D%5Cstackrel%7B%5C%25%7D%7B4.4%7D%20%5Cblacktriangleleft)
(3,5)....x1 = 3 and y1 = 5
(1,3)....x2 = 1 and y2 = 3
slope formula : (y2 - y1) / (x2 - x1)
slope = (3 - 5) / (1 - 3) = -2/-2 = 1 <== slope is 1
Never due to if they have different slopes they can only have 1 solution.
Subsitute values for x and evaluate to get values for y
when x=5, y=1
when x=0, y=-1
when x=-5, y=-3
remember, ordered pairs are in (x,y) form
so 3 ordered pairs are
(5,1)
(0,-1)
(-5,-3)
X^2+8x+15 is the area
because x+5 = length
and x +3 = width
(x+5)(x+3) =
x^2+3x+5x+15 =
x^2+8x+15 (area)