ANSWER
1a)
The given system of equation is:
![3x - 6y = - 12...(1)](https://tex.z-dn.net/?f=3x%20-%206y%20%3D%20%20-%2012...%281%29)
and
![x - 2y = - 8...(2)](https://tex.z-dn.net/?f=x%20-%202y%20%3D%20%20-%208...%282%29)
We make x the subject in equation (2) to get;
![x = 2y - 8...(3)](https://tex.z-dn.net/?f=x%20%3D%202y%20-%208...%283%29)
We put equation (3) into equation (1) to get;
![3(2y - 8) - 6y = - 12](https://tex.z-dn.net/?f=3%282y%20-%208%29%20-%206y%20%3D%20%20-%2012)
We expand the bracket to get,
![6y - 24 - 6y = - 12](https://tex.z-dn.net/?f=6y%20-%2024%20-%206y%20%3D%20%20-%2012)
![6y - 6y = 24 - 12](https://tex.z-dn.net/?f=6y%20-%206y%20%3D%2024%20-%2012)
This implies that,
![0 = 12](https://tex.z-dn.net/?f=0%20%3D%2012)
This statement is false.
Hence the system has no solution.
1b)
Let us write the two systems in the slope-intercept form;
For the first equation, we have
![3x - 6y = - 12](https://tex.z-dn.net/?f=3x%20-%206y%20%3D%20%20-%2012)
Thus implies that,
![- 6y = - 3x- 12](https://tex.z-dn.net/?f=%20-%206y%20%3D%20-%203x-%2012%20)
![y = \frac{1}{2} x + 2](https://tex.z-dn.net/?f=%20y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%202)
For the second equation, we have:
![- 2y = - x - 8](https://tex.z-dn.net/?f=%20-%20%202y%20%3D%20%20-%20x%20-%208)
![y = \frac{1}{2} x + 8](https://tex.z-dn.net/?f=%20y%20%3D%20%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%20%2B%208)
We can see that, the two equations are parallel since they have the same slope.
Also the two equations will never meet since they have different y-intercepts.
Hence the system has no solution.
Answer:
The answer is 1/6y+1/6(y+12)-2
Answer:
-4/5
Step-by-step explanation:
Lets put the equation in slope intercept form
4x+5y = -20
Subtract 4x from each side
4x-4x+5y = -4x-20
5y = -4x-20
Divide each side by 5
5y/5 = -4x/5 -20/5
y = -4/5 x -4
The equation is in the form y = mx+b where m is the slope and b is the y intercept
the slope is -4/5 and the y intercept is -4
Answer:
D. the poster will have a width of 31 2/3 inches
Step-by-step explanation:
3 1/3 • 9 1/2
10/3 • 19/2
190/6 = 31 2/3
Step-by-step explanation:
<u>Here :-</u>
- Selling price of 25 balls is equal to the Cost of 15 balls
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
<u>Let the cost price of one ball is ₹1. So ;-</u>
- Cost price of 25 balls = ₹25
- Cost price of 15 balls = ₹15
↝ Here the selling price of 25 balls is equal to the cost of 15 balls. It means C.P of 15 balls = S.P of 25 balls. So, the selling price of 25 balls is ₹15.
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
<u>Firstly, finding the loss :-</u>
![{\dashrightarrow{\sf{Loss = Cost \: Price - Selling \: Price}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%20%3D%20Cost%20%20%5C%3A%20Price%20-%20%20Selling%20%5C%3A%20%20Price%7D%7D%7D)
![{\dashrightarrow{\sf{Loss = 25 - 15}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%20%3D%2025%20-%2015%7D%7D%7D)
![{\dashrightarrow{\sf{\underline{\red{Loss =Rs.10}}}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7B%5Cunderline%7B%5Cred%7BLoss%20%3DRs.10%7D%7D%7D%7D%7D)
<em><u>∴ The loss is Rs.10.</u></em>
![\begin{gathered}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%5Cend%7Bgathered%7D)
<u>Now, finding the loss percentage :-</u>
![{\dashrightarrow{\sf{Loss\: \%= \dfrac{Loss }{Cost \: Price} \times 100}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%5C%3A%20%5C%25%3D%20%5Cdfrac%7BLoss%20%7D%7BCost%20%5C%3A%20Price%7D%20%5Ctimes%20100%7D%7D%7D)
![{\dashrightarrow{\sf{Loss\: \%= \dfrac{10 }{25} \times 100}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%5C%3A%20%5C%25%3D%20%5Cdfrac%7B10%20%7D%7B25%7D%20%5Ctimes%20100%7D%7D%7D)
![{\dashrightarrow{\sf{Loss\: \%= \dfrac{10 \times 100 }{25}}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%5C%3A%20%5C%25%3D%20%5Cdfrac%7B10%20%5Ctimes%20100%20%7D%7B25%7D%7D%7D%7D)
![{\dashrightarrow{\sf{Loss\: \%= \dfrac{1000 }{25}}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%5C%3A%20%5C%25%3D%20%5Cdfrac%7B1000%20%7D%7B25%7D%7D%7D%7D)
![{\dashrightarrow{\sf{Loss\: \%=\cancel{\dfrac{1000 }{25}}}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7BLoss%5C%3A%20%5C%25%3D%5Ccancel%7B%5Cdfrac%7B1000%20%7D%7B25%7D%7D%7D%7D%7D)
![{\dashrightarrow{\sf{\underline{\red{Loss\: \%=40 \: \%}}}}}](https://tex.z-dn.net/?f=%7B%5Cdashrightarrow%7B%5Csf%7B%5Cunderline%7B%5Cred%7BLoss%5C%3A%20%5C%25%3D40%20%5C%3A%20%5C%25%7D%7D%7D%7D%7D)
<em><u>∴ The loss percent is 40%.</u></em>
![\underline{\rule{200pt}{2.5pt}}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Crule%7B200pt%7D%7B2.5pt%7D%7D)