Question

Solve this system:
-6r+5s+2t=-11
-2r+s+4t=-9
4r-5s+5t=-4

Answer 1

`r=4\\ \\s=3\\ \\t=-1`

Explanation:

Given the system of three linear equations:

`\left\{\begin{array}{l}-6r+5s+2t=-11\\ \\-2r+s+4t=-9\\ \\4r-5s+5t=-4\end{array}\right.`

Cheange the positions of the first and the second equations:

`\left\{\begin{array}{l}-2r+s+4t=-9\\ \\-6r+5s+2t=-11\\ \\4r-5s+5t=-4\end{array}\right.`

Multiply the first equation by -3 and add it to the second equation and then multiply the first equation by 2 and add it to the third equation:

`\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-3s+13t=-22\end{array}\right.`

Multiply the second equation by 3, the third equation by 2 and add them:

`\left\{\begin{array}{r}-2r+s+4t=-9\\ \\2s-10t=16\\ \\-4t=4\end{array}\right.`

From the third equation,

`t=-1`

Substitute it into the second equation:

`2s-10\cdot (-1)=16\\ \\2s+10=16\\ \\2s=6\\ \\s=3`

Substitute
`t=-1` and
`s=3` into the first equation:

`-2r+3+4\cdot (-1)=-9\\ \\-2r+3-4=-9\\ \\-2r-1=-9\\ \\-2r=-9+1\\ \\-2r=-8\\ \\2r=8\\ \\r=4`

Hence,

`r=4\\ \\s=3\\ \\t=-1`