Answer:
![(x,y) = \left(\dfrac{18}{5},\dfrac{67}{15}\right)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%3D%20%5Cleft%28%5Cdfrac%7B18%7D%7B5%7D%2C%5Cdfrac%7B67%7D%7B15%7D%5Cright%29)
Step-by-step explanation:
First rearrange all equations into this format:
![ax+by=c](https://tex.z-dn.net/?f=ax%2Bby%3Dc)
that will result in:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![9x-7y=15](https://tex.z-dn.net/?f=9x-7y%3D15)
then we'll multiply an equation with a number such that we have same numbers on both equations (with only different signs). So we can add them
Here you can see that we've multiplied the first equation with (-3) so that we have -9x on one equation and 9x on the other. Now when we add the two equations the 9x and -9x terms will cancel out (or eliminate)
![\[\begin{array}{r@{}l@{\quad}l@{\quad}r@{}l@{}c}3x-4y&{}=-1&\xrightarrow{\times (-3)}&-9x +12y&{}=+3\\[\jot]9x -7y&{}=15&\xrightarrow{\phantom{\times (-3)}}&9x-y&{}=15&~\smash{\raisebox{.8\normalbaselineskip}{$+$}}\\\cline{4-5}&&&+5y&{}=18\\[\jot]&&&y&{}=\dfrac{18}{5}\\\end{array}\]\\](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Barray%7D%7Br%40%7B%7Dl%40%7B%5Cquad%7Dl%40%7B%5Cquad%7Dr%40%7B%7Dl%40%7B%7Dc%7D3x-4y%26%7B%7D%3D-1%26%5Cxrightarrow%7B%5Ctimes%20%28-3%29%7D%26-9x%20%2B12y%26%7B%7D%3D%2B3%5C%5C%5B%5Cjot%5D9x%20-7y%26%7B%7D%3D15%26%5Cxrightarrow%7B%5Cphantom%7B%5Ctimes%20%28-3%29%7D%7D%269x-y%26%7B%7D%3D15%26~%5Csmash%7B%5Craisebox%7B.8%5Cnormalbaselineskip%7D%7B%24%2B%24%7D%7D%5C%5C%5Ccline%7B4-5%7D%26%26%26%2B5y%26%7B%7D%3D18%5C%5C%5B%5Cjot%5D%26%26%26y%26%7B%7D%3D%5Cdfrac%7B18%7D%7B5%7D%5C%5C%5Cend%7Barray%7D%5C%5D%5C%5C)
now that we've found the value of y
we'll use this value in any of the two equations to get the value of x.
let's put y in the first equation:
![3x-4y=-1](https://tex.z-dn.net/?f=3x-4y%3D-1)
![3x-4\left( \dfrac{18}{5}\right)=-1](https://tex.z-dn.net/?f=3x-4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29%3D-1)
![3x=-1+4\left( \dfrac{18}{5}\right)](https://tex.z-dn.net/?f=3x%3D-1%2B4%5Cleft%28%20%5Cdfrac%7B18%7D%7B5%7D%5Cright%29)
![3x=-1+\dfrac{72}{5}](https://tex.z-dn.net/?f=3x%3D-1%2B%5Cdfrac%7B72%7D%7B5%7D)
![3x=\dfrac{67}{5}](https://tex.z-dn.net/?f=3x%3D%5Cdfrac%7B67%7D%7B5%7D)
![x=\dfrac{67}{3(5)}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B3%285%29%7D)
![x=\dfrac{67}{15}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B67%7D%7B15%7D)
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Partial Product is for multiplication and regrouping is for addition.
Hope that helped:)
Step-by-step explanation:
<em>it's </em><em> </em><em>absolutely </em><em>correct </em><em>.</em><em>.</em>
X= -2 is not the solution to the equation.
explanation: if you plug in -2 into -3–7, you get -1, and if you plug -2 into 5(x-1) you get -18.