Answer:
<h3>Each of the given matrix equations does not represent this system of equations.</h3>
Step-by-step explanation:
![\left\{\begin{array}{ccc}2x-3=2y\\y-5x=14\end{array}\right\\\\\text{Let's convert the system of equations to form}\\\\\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{array}\right\\\\\left\{\begin{array}{ccc}2x-3=2y&(1)\\y-5x=14&(2)\end{array}\right\\\\(1)\ 2x-3=2y\qquad\text{add 3 to both sides}\\2x=2y+3\qquad\text{subtract}\ 2y\ \text{From both sides}\\\boxed{2x-2y=3}\\(2)\ y-5x=14\\\boxed{-5x+y=14}\\\\\text{We get the system of equations in the form we need.}](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-3%3D2y%5C%5Cy-5x%3D14%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BLet%27s%20convert%20the%20system%20of%20equations%20to%20form%7D%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Da_1x%2Bb_1y%3Dc_1%5C%5Ca_2x%2Bb_2y%3Dc_2%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-3%3D2y%26%281%29%5C%5Cy-5x%3D14%26%282%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%281%29%5C%202x-3%3D2y%5Cqquad%5Ctext%7Badd%203%20to%20both%20sides%7D%5C%5C2x%3D2y%2B3%5Cqquad%5Ctext%7Bsubtract%7D%5C%202y%5C%20%5Ctext%7BFrom%20both%20sides%7D%5C%5C%5Cboxed%7B2x-2y%3D3%7D%5C%5C%282%29%5C%20y-5x%3D14%5C%5C%5Cboxed%7B-5x%2By%3D14%7D%5C%5C%5C%5C%5Ctext%7BWe%20get%20the%20system%20of%20equations%20in%20the%20form%20we%20need.%7D)
![\left\{\begin{array}{ccc}2x-2y=3\\-5x+y=14\end{array}\right\\\\\text{The first matrix is the matrix of coefficients at x and y.}\\\\\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\end{array}\right] \Rightarrow\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right]\\\\\text{The second matrix is the matrix:}\\\\\left[\begin{array}{ccc}x\\y\end{array}\right]\\\\\text{The third matrix is the matrix of numbers from the right side of the equation.}\\\\\left[\begin{array}{ccc}c_1\\c_2\end{array}\right]\Rightarrow\left[\begin{array}{ccc}3\\14\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D2x-2y%3D3%5C%5C-5x%2By%3D14%5Cend%7Barray%7D%5Cright%5C%5C%5C%5C%5Ctext%7BThe%20first%20matrix%20is%20the%20matrix%20of%20coefficients%20at%20x%20and%20y.%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da_1%26b_1%5C%5Ca_2%26b_2%5Cend%7Barray%7D%5Cright%5D%20%5CRightarrow%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-2%5C%5C-5%261%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BThe%20second%20matrix%20is%20the%20matrix%3A%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Ctext%7BThe%20third%20matrix%20is%20the%20matrix%20of%20numbers%20from%20the%20right%20side%20of%20the%20equation.%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc_1%5C%5Cc_2%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C14%5Cend%7Barray%7D%5Cright%5D)
![\text{Therefore we have:}\\\\\left[\begin{array}{ccc}2&-2\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}3\\14\end{array}\right]](https://tex.z-dn.net/?f=%5Ctext%7BTherefore%20we%20have%3A%7D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-2%5C%5C-5%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C14%5Cend%7Barray%7D%5Cright%5D)
<span>First find how many grams are in 15.87kg and how many meters are in 30.48cm
15.87kg x 1000g/kg = 15, 870g
30.49cm x 1m/100cm = 0.3049m
Then, set up a proportion.
0.3049m/15, 870g = 1m/x g
Cross multiply to get..
0.3049x = 15, 870
Divide for x and there you are.</span>Source(s):Myself.1004 <span>· 8 years ago
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