Step-by-step explanation:
If you lost "y" in the first equation.
![\underline{+\left\{\begin{array}{ccc}2x-3y=14\\-x+3y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\\\.\qquad x=8\\\\\text{Put the value of x to the first equation:}\\\\2(8)-3y=14\\16-3y=14\qquad\text{subtract 16 from both sides}\\-3y=-2\qquad\text{divide both sides by (-3)}\\y=\dfrac{2}{3}\\\boxed{x=8,\ y=\dfrac{2}{3}}](https://tex.z-dn.net/?f=%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-3y%3D14%5C%5C-x%2B3y%3D-6%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C%5C%5C.%5Cqquad%20x%3D8%5C%5C%5C%5C%5Ctext%7BPut%20the%20value%20of%20x%20to%20the%20first%20equation%3A%7D%5C%5C%5C%5C2%288%29-3y%3D14%5C%5C16-3y%3D14%5Cqquad%5Ctext%7Bsubtract%2016%20from%20both%20sides%7D%5C%5C-3y%3D-2%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%20%28-3%29%7D%5C%5Cy%3D%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5Cboxed%7Bx%3D8%2C%5C%20y%3D%5Cdfrac%7B2%7D%7B3%7D%7D)
If first equation is correct.
![2x-3=14\qquad\text{add 3 to both sides}\\2x=17\qquad\text{divide both sides by 2}\\x=8.5\\\\\text{Put the value of x to the second equation:}\\-8.5+3y=-6\qquad\text{add 8.5 to both sides}\\3y=2.5\qquad\text{divide both sides by 3}\\y=\dfrac{2.5}{3}\\y=\dfrac{25}{30}\\y=\dfrac{5}{6}\\\\\boxed{x=8.5,\ y=\dfrac{5}{6}}](https://tex.z-dn.net/?f=2x-3%3D14%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C2x%3D17%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5Cx%3D8.5%5C%5C%5C%5C%5Ctext%7BPut%20the%20value%20of%20x%20to%20the%20second%20equation%3A%7D%5C%5C-8.5%2B3y%3D-6%5Cqquad%5Ctext%7Badd%208.5%20to%20both%20sides%7D%5C%5C3y%3D2.5%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%203%7D%5C%5Cy%3D%5Cdfrac%7B2.5%7D%7B3%7D%5C%5Cy%3D%5Cdfrac%7B25%7D%7B30%7D%5C%5Cy%3D%5Cdfrac%7B5%7D%7B6%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D8.5%2C%5C%20y%3D%5Cdfrac%7B5%7D%7B6%7D%7D)
Answer:-19
Step-by-step explanation:
Answer:
7 oz, 13 sandwiches, 22.75 oz, and 30.33 oz.
Step-by-step explanation:
Answer:
10 nickels and 10 quarters
Step-by-step explanation:
Given
Number of coins: 20
Vaiue of coins = $3.00
Required
Number of Nickels and Quarters;
<em>Let N =Nickels and Q =Quarters</em>
The total coins is represented as:
![N + Q = 20](https://tex.z-dn.net/?f=N%20%2B%20Q%20%3D%2020)
1 nickel is equivalent to $0.05 and 1 quarter is equivalent to $0.25; So
![0.05N + 0.25Q = 3](https://tex.z-dn.net/?f=0.05N%20%2B%200.25Q%20%3D%203)
Make N the subject of formula in the first equation
![N = 20 - Q](https://tex.z-dn.net/?f=N%20%3D%2020%20-%20Q)
Substitute this in the second equation
![0.05(20 - Q) + 0.25Q = 3](https://tex.z-dn.net/?f=0.05%2820%20-%20Q%29%20%2B%200.25Q%20%3D%203)
![1 - 0.05Q + 0.25Q = 3](https://tex.z-dn.net/?f=1%20-%200.05Q%20%2B%200.25Q%20%3D%203)
Collect like terms
![-0.05Q + 0.25Q = 3 - 1](https://tex.z-dn.net/?f=-0.05Q%20%2B%200.25Q%20%3D%203%20-%201)
![0.2Q = 2](https://tex.z-dn.net/?f=0.2Q%20%3D%202)
Multiply both sides by 5
![5 * 0.2Q = 2 * 5](https://tex.z-dn.net/?f=5%20%2A%200.2Q%20%3D%202%20%2A%205)
![Q = 10](https://tex.z-dn.net/?f=Q%20%3D%2010)
Recall that N = 20 - Q
![N = 20 - 10](https://tex.z-dn.net/?f=N%20%3D%2020%20-%2010)
![N = 10](https://tex.z-dn.net/?f=N%20%3D%2010)
The answer is B, because the numbers in the equation are 2, and -3x. The signs have to stay with the numbers they are with. So if you move the 3 to the front you have to keep the negative with it.