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23-08-2014
Mathematics

Answered

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

X + 3y = 9

3x –y = 7

Answer :

24-08-2014

[tex]After\ adding\ equations\ and\ simplifying:\\\\One\ solution:\\\\x=number\\ example: x=2\\\\ infinitely\ many\ solutions:\\\\ Left\ side=\ Right\ side\\ example:\\ 2=2\\\\ No\ solutions:\\\\2 \neq 5[/tex][tex] \left \{ {{x+3y=9} \atop {3x-y=7}\ \ |*3} \right.\\\\ \left \{ {{x+3y=9} \atop {9x-3y=21}} \right.\\+--------\\\\Addition\ method:\\\\10x=30\ \ |:10 \\\\x=3\\\\x+3y=9\\\\3y =9-x=9-3=6\\\\y=2\\\\ \left \{ {{y=2} \atop {x=3}} \right. [/tex]

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