Simultaneous equations can be solved by substitution, elimination, graphs and by matrices.
The values of x, y and z are:
- [tex]\mathbf{x =3}[/tex].
- [tex]\mathbf{y = 6}[/tex].
- [tex]\mathbf{z = -1}[/tex]
The equations are given as:
[tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-4x + 4y +5z = 7}[/tex]
[tex]\mathbf{2x +2z = 4}[/tex]
Make z the subject in [tex]\mathbf{2x +2z = 4}[/tex]
[tex]\mathbf{2z = 4 - 2x}[/tex]
Divide by 2
[tex]\mathbf{z = 2 - x}[/tex]
Substitute [tex]\mathbf{z = 2 - x}[/tex] in [tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-x - y -z = -8}[/tex]
[tex]\mathbf{-x - y - (2-x) = -8}[/tex]
[tex]\mathbf{-x - y - 2+x = -8}[/tex]
Cancel out common terms
[tex]\mathbf{- y - 2 = -8}[/tex]
Add 2 to both sides
[tex]\mathbf{- y = -8+2}[/tex]
[tex]\mathbf{- y = -6}[/tex]
Divide by -1
[tex]\mathbf{y = 6}[/tex]
Substitute [tex]\mathbf{z = 2 - x}\mathbf{\ and\ y = 6}[/tex] in [tex]\mathbf{-4x + 4y +5z = 7}[/tex]
[tex]\mathbf{-4x + 4 \times 6 + 5 \times (2 - x) = 7}[/tex]
[tex]\mathbf{-4x + 24 + 5 \times (2 - x) = 7}[/tex]
Open brackets
[tex]\mathbf{-4x + 24 + 10 - 5x = 7}[/tex]
Collect like terms
[tex]\mathbf{-4x - 5x =- 24 - 10 + 7}[/tex]
[tex]\mathbf{-9x =-27}[/tex]
Divide through by -9
[tex]\mathbf{x =3}[/tex]
Recall that: [tex]\mathbf{z = 2 - x}[/tex]
So, we have:
[tex]\mathbf{z = 2-3}[/tex]
[tex]\mathbf{z = -1}[/tex]
Hence, the results are:
[tex]\mathbf{x =3}[/tex]
[tex]\mathbf{y = 6}[/tex]
[tex]\mathbf{z = -1}[/tex]
Read more about simultaneous equations at:
https://brainly.com/question/10852714
