I would go with option C. x, in the first equation.
The X term has a coefficient of 3, the lowest common factor amongst the 3 terms making for easy isolation of the variable.
Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Candies with celias and emmas is 60 and 45 respectively.
<u>Solution:</u>
Given, Getting home from trick or treat celia and emma counted their candies. Half of celias candies is equal to 2/3 of emmas candies.
They had a total of 105 candies altogether.
We have to find how many candies did each of them have.
Let the number of candies with celias be n, then number of candies with emma will be 105 – n.
Now according to given condition.
![\begin{array}{l}{\frac{1}{2} \times \text { celias candies count }=\frac{2}{3} \times \text { emmas candies count }} \\\\ {\rightarrow \frac{1}{2} \times n=\frac{2}{3} \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 \times n=2 \times 2 \times(105-n)} \\\\ {\rightarrow 3 n=4(105-n)} \\\\ {\quad \rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n=420-4 n} \\\\ {\rightarrow 3 n+4 n=420} \\\\ {\rightarrow 7 n=7 \times 60} \\\\ {\rightarrow n=60}\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bl%7D%7B%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Ctext%20%7B%20celias%20candies%20count%20%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%20%5Ctext%20%7B%20emmas%20candies%20count%20%7D%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20n%3D%5Cfrac%7B2%7D%7B3%7D%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20%5Ctimes%20n%3D2%20%5Ctimes%202%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20%5Ctimes%20n%3D2%20%5Ctimes%202%20%5Ctimes%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%3D4%28105-n%29%7D%20%5C%5C%5C%5C%20%7B%5Cquad%20%5Crightarrow%203%20n%3D420-4%20n%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%3D420-4%20n%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%203%20n%2B4%20n%3D420%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%207%20n%3D7%20%5Ctimes%2060%7D%20%5C%5C%5C%5C%20%7B%5Crightarrow%20n%3D60%7D%5Cend%7Barray%7D)
Hence, candies with celias and emmas is 60 and 45 respectively.
6=3 : 16=6 14=6 that should be right