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Sagot :
The given system expressed as a matrix would be
0 4 -1 -5
1 5 1 -3
2 -1 3 13
To solve this, first, we have to change the first row for the second
1 5 1 -3
0 4 -1 -5
2 -1 3 13
Now, we multiply the first row by 2, then subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 -11 1 19
Then, we multiple the second row with -11/4 to subtract it from the third row.
1 5 1 -3
0 4 -1 -5
0 0 -7/4 21/4
The resulting system would be
[tex]\mleft\{\begin{aligned}x+5y+z=-3 \\ 4y-z=-5 \\ -\frac{7}{4}z=\frac{21}{4}\end{aligned}\mright.[/tex]We solve for z
[tex]\begin{gathered} \frac{-7}{4}z=\frac{21}{4} \\ z=\frac{21}{-7}=-3 \end{gathered}[/tex]Therefore, z is equal to -3.
We use z to find y in the second equation.
[tex]\begin{gathered} 4y-(-3)=-5 \\ 4y+3=-5 \\ 4y=-5-3 \\ 4y=-8 \\ y=\frac{-8}{4}=-2 \end{gathered}[/tex]Therefore, y is equal to -2.
We use y and z to find x in the first equation.
[tex]\begin{gathered} x+5(-2)+(-3)=-3 \\ x-10-3=-3 \\ x=-3+10+3=10 \end{gathered}[/tex]Therefore, x is equal to 10.
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