We have the 2 equations
1- ) 5x-8y=6
2-) -6x-3y=18
multiplying the first equation by 3 and the second equation by 8 then subtracting
1-) 15x-24y=18
2-) -48x-24y=144
-48x-24y=144
(-) 15x-24y=18
-------------------------------------
-63x = 126
x=-2
substituting in equation 1
5(-2)-8y=6
-10-8y=6
-8y=16
y=-2
the soultion is (-2,-2)
Answer:
(0, -3), (-1, 1)
Step-by-step explanation:
The equation can be simplified to a form more helpful for graphing.
Subtract 7:
24x +18 = -6y
We note that all of the coefficients are multiples of 6, so we can divide by -6:
y = -4x -3
This is slope-intercept form, so it tells you that the y-intercept is -3, which means one point on the graph is (0, -3).
The slope is -4, so an x-value in the negative direction will give a more positive y-value. We can choose x=-1 and find y:
y = -4(-1) -3 = 4 -3 = 1
Then another point on the graph is (-1, 1).
Two points on the graph are (0, -3) and (-1, 1).
-- They're losing employees . . . so you know that the line will slope down, and
its slope is negative;
-- They're losing employees at a steady rate . . . so you know that the slope is
the same everywhere on the line; this tells you that the graph is a straight line.
I can see the function right now, but I'll show you how to go through the steps to
find the function. I need to point out that these are steps that you've gone through
many times, but now that the subject pops up in a real-world situation, suddenly
you're running around in circles with your hair on fire screaming "What do I do ?
Somebody give me the answer !".
Just take a look at what has already been handed to you:
0 months . . . 65 employees
1 month . . . . 62 employees
2 months . . . 59 employees
You know three points on the line !
(0, 65) , (1, 62) , and (2, 59) .
For the first point, 'x' happens to be zero, so immediately
you have your y-intercept ! ' b ' = 65 .
You can use any two of the points to find the slope of the line.
You will calculate that the slope is negative-3 . . . which you
might have realized as you read the story, looked at the numbers,
and saw that they are <u>firing 3 employees per month</u>.
("Losing" them doesn't quite capture the true spirit of what is happening.)
So your function ... call it ' W(n) ' . . . Workforce after 'n' months . . .
is <em>W(n) = 65 - 3n</em> .
Answer:
a plane
Step-by-step explanation:
from the provided focus point and directrix, we can see that the focus point is above the directrix, meaning is a vertical parabola and is opening upwards, thus the squared variable will be the "x".
keeping in mind the vertex is half-way between these two fellows, Check the picture below.
![\bf \textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvertical%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28y-%20k%29%3D%28x-%20h%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Ck%2Bp%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7By%3Dk-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \begin{cases} h = 7\\ k = 7\\ p = 2 \end{cases}\implies 4(2)(y-7)=(x-7)^2\implies 8(y-7)=(x-7)^2 \\\\\\ y-7=\cfrac{1}{8}(x-7)^2\implies \boxed{y=\cfrac{1}{8}(x-7)^2+7}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20h%20%3D%207%5C%5C%20k%20%3D%207%5C%5C%20p%20%3D%202%20%5Cend%7Bcases%7D%5Cimplies%204%282%29%28y-7%29%3D%28x-7%29%5E2%5Cimplies%208%28y-7%29%3D%28x-7%29%5E2%20%5C%5C%5C%5C%5C%5C%20y-7%3D%5Ccfrac%7B1%7D%7B8%7D%28x-7%29%5E2%5Cimplies%20%5Cboxed%7By%3D%5Ccfrac%7B1%7D%7B8%7D%28x-7%29%5E2%2B7%7D)