
Change x to y, and y to x.

solve for y:

Your answer is:

Answer:
The set of solutions is ![\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%5C%5Cb%5C%5Cx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-26%2B503y%2B543z%5C%5C-37%2B655y%2B724z%5C%5C-4%2B80y%2B90z%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3A%20%5Ctext%7By%2C%20z%20are%20real%20numbers%7D%5C%7D)
Step-by-step explanation:
The matrix associated to the problem is
and the vector of independent terms is (3,1,-1)^t. Then the matrix equation form of the system is Ax=b.
The vector equation form is
.
Now we solve the system.
The aumented matrix of the system is
.
Applying rows operations we obtain a echelon form of the matrix, that is ![\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\0&1&-8&-15&-4&-5\\0&0&1&-80&-9&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccccc%7D1%26-1%262%26-8%261%263%5C%5C0%261%26-8%26-15%26-4%26-5%5C%5C0%260%261%26-80%26-9%26-4%5Cend%7Barray%7D%5Cright%5D)
Now we solve for the unknown variables:
- x-80y-90z=-4 then x=-4+80y+90z
- b-8x-15y-4z=-5, b-8(-4+80y+90z)-15y-4z=-5 then b=-37+655y+724z.
- a-b+2x-8y+z=3, a-(-37+655y+724z)+2(-4+80y+90z)-8y+z=3, then a=-26+503y+543z
Since the system has two free variables then has infinite solutions.
The set of solutions is ![\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}](https://tex.z-dn.net/?f=%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%5C%5Cb%5C%5Cx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-26%2B503y%2B543z%5C%5C-37%2B655y%2B724z%5C%5C-4%2B80y%2B90z%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3A%20%5Ctext%7By%2C%20z%20are%20real%20numbers%7D%5C%7D)
................................................i dont know