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linear equations in deletion method2x + 2y − z = 04y − z = 1−x − 2y + z = 2

Sagot :

The given system is:

[tex]\begin{gathered} 2x+2y-z=0\ldots(i) \\ 4y-z=1\ldots(ii) \\ -x-2y+z=2\ldots(iii) \end{gathered}[/tex]

Multipliy (iii) by 2 to get:

[tex]-2x-4y+2z=4\ldots.(iv)[/tex]

Add (i) and (iv)

[tex]\begin{gathered} 2x+2y-z=0 \\ + \\ -2x-4y+2z=4 \\ -2y+z=4\ldots(v) \end{gathered}[/tex]

Add (ii) and (v) to get:

[tex]\begin{gathered} 4y-z=1 \\ + \\ -2y+z=4 \\ 2y=5 \\ y=\frac{5}{2} \end{gathered}[/tex]

Put y=5/2 in (ii) to get:

[tex]\begin{gathered} 4(\frac{5}{2})-z=1 \\ 10-z=1 \\ -z=-9 \\ z=9 \end{gathered}[/tex]

Put y=5/2 and z=9 in (i) to get:

[tex]\begin{gathered} 2x+2(\frac{5}{2})-9=0 \\ 2x+5-9=0 \\ 2x=4 \\ x=2 \end{gathered}[/tex]

Hence x=2, y=5/2 and z=9.

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