Step-by-step explanation:
![1.\\\left\{\begin{array}{ccc}y=3x&(1)\\2y=6x&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\2(3x)=6x\\6x=6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\6x-6x=6x-6x\\0=0\qquad\text{TRUE}\\\\Answer:\ \text{Infinitely many solutions}\\\\\left\{\begin{array}{ccc}y=3x\\x\in\mathbb{R}\end{array}\right](https://tex.z-dn.net/?f=1.%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3D3x%26%281%29%5C%5C2y%3D6x%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%281%29%20to%20%282%29%3A%7D%5C%5C%5C%5C2%283x%29%3D6x%5C%5C6x%3D6x%5Cqquad%5Ctext%7Bsubtract%7D%5C%206x%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C6x-6x%3D6x-6x%5C%5C0%3D0%5Cqquad%5Ctext%7BTRUE%7D%5C%5C%5C%5CAnswer%3A%5C%20%5Ctext%7BInfinitely%20many%20solutions%7D%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3D3x%5C%5Cx%5Cin%5Cmathbb%7BR%7D%5Cend%7Barray%7D%5Cright)
![2.\\\left\{\begin{array}{ccc}y=2x+5&(1)\\y-2x=1&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\(2x+5)-2x=1\\2x+5-2x=1\qquad\text{combine like terms}\\(2x-2x)+5=1\\5=-1\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}](https://tex.z-dn.net/?f=2.%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Dy%3D2x%2B5%26%281%29%5C%5Cy-2x%3D1%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BSubstitute%20%281%29%20to%20%282%29%3A%7D%5C%5C%5C%5C%282x%2B5%29-2x%3D1%5C%5C2x%2B5-2x%3D1%5Cqquad%5Ctext%7Bcombine%20like%20terms%7D%5C%5C%282x-2x%29%2B5%3D1%5C%5C5%3D-1%5Cqquad%5Ctext%7BFALSE%7D%5C%5C%5C%5CAnswer%3A%5C%20%5Ctext%7BNo%20solution.%7D)
![3.\\\left\{\begin{array}{ccc}3x-2y=9\\-6x+4y=1&\text{divide both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x-2y=9\\-3x+2y=0.5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad0=9.5\qquad\text{FALSE}\\\\Answer:\ \text{No solution.}](https://tex.z-dn.net/?f=3.%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D3x-2y%3D9%5C%5C-6x%2B4y%3D1%26%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5Cend%7Barray%7D%5Cright%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D3x-2y%3D9%5C%5C-3x%2B2y%3D0.5%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C.%5Cqquad%5Cqquad0%3D9.5%5Cqquad%5Ctext%7BFALSE%7D%5C%5C%5C%5CAnswer%3A%5C%20%5Ctext%7BNo%20solution.%7D)
Answer: 1:21
Step-by-step explanation:
We know that if they say students they mean both boys and girls so we add 11 and 10 to make 21 and since its, (COACH,) and then student we do 1:21 and not 21:1!
Answer: x^3 - 1/x^3 - 2x + 2/x
It cannot be factorized.
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
We can set up equation for this one.
Let's say the number is X.
the sum of X and 14 can be expressed as : X+14
five times the sum of X and 14 can be expressed as 5(x+14)
and 5(X+14) = 80
![5(x+14) = 80\\x+14 = 80 \div 5 = 16\\x = 16-14 = 2](https://tex.z-dn.net/?f=5%28x%2B14%29%20%3D%2080%5C%5Cx%2B14%20%3D%2080%20%5Cdiv%205%20%3D%2016%5C%5Cx%20%3D%2016-14%20%3D%202)
The number is 2
Answer:
g = 6
Step-by-step explanation:
5.2g + 10 = 2.2g + 28 (Given)
3g + 10 = 28 (Subtracted 2.2g on both sides)
3g = 18 (Subtracted 10 on both sides)
g = 6 (Divided 3 on both sides)
To check to make sure you are correct, simply substitute your answer for g:
5.2(6) + 10 = 2.2(6) + 28
31.2 + 10 = 13.2 + 28
41.2 = 41.2
You'll know you're correct if they both equal the same. In this case, the solution works.