Answer:
To answer this question one can do either one of two methods one of which is elimination, or substitution:
Step-by-step explanation:
One these methods is two fold and that is one can be done with linear algebra which can represent the system of equations using a augmented matrix.
![4x+y=2\\-x+y=-3](https://tex.z-dn.net/?f=4x%2By%3D2%5C%5C-x%2By%3D-3)
Now we can setup the Gauss-elimination using row echelon form:
![\left[\begin{array}{ccc}4&1&|+2\\-1&1&|-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%26%7C%2B2%5C%5C-1%261%26%7C-3%5Cend%7Barray%7D%5Cright%5D)
The first thing we are gonna do is perform the indicated row operation
![\frac{1}4R_1+R_2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D4R_1%2BR_2)
Which gives you the following:
![\left[\begin{array}{ccc}4&1&|+2\\0&\frac{5}4&|-\frac{5}2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%26%7C%2B2%5C%5C0%26%5Cfrac%7B5%7D4%26%7C-%5Cfrac%7B5%7D2%5Cend%7Barray%7D%5Cright%5D)
Now we must perform another row operation
![4*R_2](https://tex.z-dn.net/?f=4%2AR_2)
![\left[\begin{array}{ccc}4&1&|2\\ 0 &5&|-10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%261%26%7C2%5C%5C%200%20%265%26%7C-10%5Cend%7Barray%7D%5Cright%5D)
Next row operation is the following:
![R_1-\frac{1}5R_2](https://tex.z-dn.net/?f=R_1-%5Cfrac%7B1%7D5R_2)
Which produces the following matrix
![\left[\begin{array}{ccc}4&0&|4\\0&5&|-10\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%260%26%7C4%5C%5C0%265%26%7C-10%5Cend%7Barray%7D%5Cright%5D)
Then chain in these two row operations and you get the following:
![\frac{R_1}4\\\frac{R_2}5](https://tex.z-dn.net/?f=%5Cfrac%7BR_1%7D4%5C%5C%5Cfrac%7BR_2%7D5)
Which produces this matrix:
![\left[\begin{array}{ccc}1&0&1\\0&1&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%261%5C%5C0%261%26-2%5Cend%7Barray%7D%5Cright%5D)
Which means the ordered pair is the following:
is the solution