System 3x3 – Solved Problems Database

All the problems and solutions shown below were generated using the System 3x3 calculator.

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ID	Problem	Count
51	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&-~~~~~ y&-~~~~~ z&~=~0\\2~ x&+~~~~ y&&~=~7\\-1~ x&&+~~5~ z&~=~9\end{array}$$	21
52	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~3~ z&~=~11\\2~ x&+~~~~ y&-~~~2~ z&~=~9\\4~ x&+~~3~ y&+~~~~ z&~=~16\end{array}$$	20
53	Solve system of equations using Elimination method $$\begin{array}{ cccc }3~ x&+~~7~ y&+~~9~ z&~=~1236\\9~ x&+~~5~ y&+~~~~ z&~=~990\\6~ x&+~~6~ y&+~~5~ z&~=~1113\end{array}$$	20
54	Solve system of equations using Elimination method $$\begin{array}{ cccc }-1~ x&-~~~5~ y&+~~~~ z&~=~17\\-5~ x&-~~~5~ y&+~~5~ z&~=~5\\2~ x&+~~5~ y&-~~~3~ z&~=~-10\end{array}$$	20
55	Solve system of equations using Elimination method $$\begin{array}{ cccc }4~ x&+~~4~ y&+~~8~ z&~=~2200\\0.12~ x&+~~0.16~ y&+~~0.12~ z&~=~66\\0.16~ x&+~~0.2~ y&+~~0.2~ z&~=~88\end{array}$$	19
56	Solve system of equations using Elimination method $$\begin{array}{ cccc }-4~ x&-~~~5~ y&-~~~~~ z&~=~18\\-2~ x&-~~~5~ y&-~~~2~ z&~=~12\\-2~ x&+~~5~ y&+~~2~ z&~=~4\end{array}$$	19
57	Solve system of equations using Cramers rule $$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~2\\~~ x&-~~~~~ y&+~~2~ z&~=~5\\2~ x&+~~2~ y&+~~2~ z&~=~12\end{array}$$	19
58	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~4~ y&-~~~3~ z&~=~12\\3~ x&-~~~2~ y&+~~2~ z&~=~-9\\-1~ x&+~~~~ y&-~~~3~ z&~=~0\end{array}$$	18
59	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~4~ y&+~~6~ z&~=~1000\\3~ x&+~~7~ y&+~~10~ z&~=~1600\\5~ x&+~~9~ y&+~~14~ z&~=~2400\end{array}$$	18
60	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~1.5~ y&+~~3~ z&~=~14.5\\~~ x&+~~~~ y&+~~4~ z&~=~12\\2.5~ x&+~~3~ y&+~~~~ z&~=~15\end{array}$$	18
61	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~~~ y&-~~~2~ z&~=~-1\\3~ x&-~~~3~ y&-~~~~~ z&~=~5\\~~ x&-~~~2~ y&+~~3~ z&~=~6\end{array}$$	17
62	Solve system of equations using Elimination method $$\begin{array}{ cccc }3~ x&+~~3~ y&+~~6~ z&~=~9\\~~ x&+~~3~ y&+~~2~ z&~=~5\\3~ x&+~~12~ y&+~~12~ z&~=~18\end{array}$$	17
63	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~~~ y&+~~~~ z&~=~3\\~~ x&-~~~~~ y&+~~3~ z&~=~20\\4~ x&+~~2~ y&+~~~~ z&~=~1\end{array}$$	17
64	Solve system of equations using Elimination method $$\begin{array}{ cccc }4~ x&+~~4~ y&+~~~~ z&~=~24\\2~ x&-~~~4~ y&+~~~~ z&~=~0\\5~ x&-~~~4~ y&-~~~5~ z&~=~12\end{array}$$	17
65	Solve system of equations using Elimination method $$\begin{array}{ cccc }20~ x&+~~5~ y&+~~90~ z&~=~1550\\3~ x&+~~~~ y&+~~3~ z&~=~140\\4~ x&+~~2~ y&+~~13~ z&~=~310\end{array}$$	17
66	Solve system of equations using Elimination method $$\begin{array}{ cccc }4~ x&+~~3~ y&+~~6~ z&~=~1800\\0.1~ x&+~~0.15~ y&+~~0.05~ z&~=~40\\0.1~ x&+~~0.1~ y&+~~0.2~ z&~=~50\end{array}$$	17
67	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~~~ y&+~~~~ z&~=~109\\~~ x&&-~~~~~ z&~=~-6\\&~~ y&-~~~3~ z&~=~0\end{array}$$	16
68	Solve system of equations using Elimination method $$\begin{array}{ cccc }140~ x&-~~~50~ y&-~~~30~ z&~=~80\\-50~ x&+~~100~ y&-~~~40~ z&~=~70\\-30~ x&-~~~40~ y&+~~90~ z&~=~0\end{array}$$	16
69	Solve system of equations using Elimination method $$\begin{array}{ cccc }13~ x&+~~6~ y&+~~3~ z&~=~99\\2~ x&+~~9~ y&+~~3~ z&~=~40.5\\&&0&~=~38\end{array}$$	16
70	Solve system of equations using Elimination method $$\begin{array}{ cccc }3~ x&+~~2~ y&&~=~0\\5~ x&+~~6~ y&+~~7~ z&~=~8\\-2~ x&+~~3~ y&+~~4~ z&~=~12\end{array}$$	16
71	Solve system of equations using Elimination method $$\begin{array}{ cccc }4~ x&-~~~2~ y&+~~2~ z&~=~12\\3~ x&+~~2~ y&+~~4~ z&~=~10\\2~ x&-~~~~~ y&+~~~~ z&~=~7\end{array}$$	16
72	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&-~~~6~ y&+~~4~ z&~=~-12\\~~ x&+~~~~ y&-~~~4~ z&~=~12\\2~ x&+~~2~ y&+~~5~ z&~=~-15\end{array}$$	16
73	Solve system of equations using Elimination method $$\begin{array}{ cccc }12~ x&+~~8~ y&+~~6~ z&~=~1180\\4~ x&+~~10~ y&+~~4~ z&~=~900\\4~ x&+~~2~ y&+~~10~ z&~=~920\end{array}$$	16
74	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~~~ y&-~~~~~ z&~=~-1\\2~ x&-~~~2~ y&+~~3~ z&~=~8\\2~ x&-~~~~~ y&+~~2~ z&~=~9\end{array}$$	15
75	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&-~~~3~ y&-~~~2~ z&~=~4\\~~ x&+~~3~ y&+~~2~ z&~=~-7\\-4~ x&-~~~4~ y&-~~~2~ z&~=~10\end{array}$$	15
76	Solve system of equations using Elimination method $$\begin{array}{ cccc }0.12~ x&+~~0.16~ y&+~~0.12~ z&~=~66\\0.16~ x&+~~0.2~ y&+~~0.2~ z&~=~88\\4~ x&+~~4~ y&+~~8~ z&~=~2200\end{array}$$	15
77	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~2~ y&+~~2~ z&~=~2\\~~ x&+~~~~ y&+~~3~ z&~=~5\\~~ x&+~~4~ y&+~~~~ z&~=~10\end{array}$$	15
78	Solve system of equations using Elimination method $$\begin{array}{ cccc }8~ x&+~~12~ y&+~~4~ z&~=~415.8\\~~ x&-~~~10~ y&&~=~13.09\\&~~ y&-~~~~~ z&~=~-6\end{array}$$	15
79	Solve system of equations using Elimination method $$\begin{array}{ cccc }5~ x&+~~10~ y&+~~15~ z&~=~60\\2~ x&+~~4~ y&+~~6~ z&~=~60\\~~ x&+~~2~ y&+~~3~ z&~=~60\end{array}$$	15
80	Solve system of equations using Cramers rule $$\begin{array}{ cccc }-1~ x&-~~~5~ y&+~~~~ z&~=~17\\-5~ x&-~~~5~ y&+~~5~ z&~=~5\\2~ x&+~~5~ y&-~~~3~ z&~=~-10\end{array}$$	15
81	Solve system of equations using Elimination method $$\begin{array}{ cccc }2~ x&+~~3~ y&+~~4~ z&~=~52\\~~ x&+~~2~ y&+~~3~ z&~=~36\\5~ x&+~~~~ y&+~~~~ z&~=~20\end{array}$$	15
82	Solve system of equations using Elimination method $$\begin{array}{ cccc }5~ x&+~~5~ y&+~~5~ z&~=~-20\\4~ x&+~~3~ y&+~~3~ z&~=~-6\\-4~ x&+~~3~ y&+~~3~ z&~=~9\end{array}$$	15
83	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~~~ y&+~~~~ z&~=~4\\~~ x&+~~~~ y&-~~~~~ z&~=~4\\3~ x&+~~3~ y&+~~~~ z&~=~12\end{array}$$	15
84	Solve system of equations using Elimination method $$\begin{array}{ cccc }13~ x&+~~6~ y&+~~3~ z&~=~99\\2~ x&+~~9~ y&+~~3~ z&~=~40.5\\~~ x&+~~~~ y&+~~~~ z&~=~38\end{array}$$	15
85	Solve system of equations using Elimination method $$\begin{array}{ cccc }13~ x&+~~6~ y&+~~3~ z&~=~99\\2~ x&+~~9~ y&+~~3~ z&~=~40.5\\~~ x&+~~~~ y&+~~~~ z&~=~10.5\end{array}$$	15
86	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~5~ y&+~~5~ z&~=~2923\\9~ x&+~~7~ y&+~~3~ z&~=~7097\\5~ x&+~~6~ y&+~~4~ z&~=~5010\end{array}$$	15
87	Solve system of equations using Elimination method $$\begin{array}{ cccc }3~ x&+~~10~ y&-~~~12~ z&~=~40\\~~ x&-~~~5~ y&&~=~0\\~~ x&&-~~~4~ z&~=~0\end{array}$$	15
88	Solve system of equations using Elimination method $$\begin{array}{ cccc }3~ x&+~~2~ y&+~~4~ z&~=~1160\\2~ x&+~~~~ y&+~~4~ z&~=~800\\6~ x&+~~~~ y&+~~12~ z&~=~1920\end{array}$$	15
89	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~2~ y&+~~~~ z&~=~9\\~~ x&-~~~~~ y&+~~3~ z&~=~13\\&&2~ z&~=~10\end{array}$$	15
90	Solve system of equations using Elimination method $$\begin{array}{ cccc }200~ x&+~~50~ y&+~~250~ z&~=~8450\\~~ x&+~~~~ y&+~~~~ z&~=~45\\30~ x&+~~15~ y&+~~12~ z&~=~720\end{array}$$	15
91	Solve system of equations using Elimination method $$\begin{array}{ cccc }0.2~ x&+~~0.7~ y&+~~0.1~ z&~=~81\\0.5~ x&+~~0.3~ y&+~~0.2~ z&~=~83\\0.1~ x&+~~0.4~ y&+~~0.5~ z&~=~76\end{array}$$	15
92	Solve system of equations using Elimination method $$\begin{array}{ cccc }-1~ x&-~~~5~ y&-~~~5~ z&~=~2\\4~ x&-~~~5~ y&+~~4~ z&~=~19\\&5~ y&&~=~-20\end{array}$$	15
93	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~~~ y&+~~~~ z&~=~1\\-1~ x&+~~\dfrac{ 2 }{ 3 }~ y&+~~\dfrac{ 2 }{ 3 }~ z&~=~0\\~~ x&-~~~~~ y&+~~\dfrac{ 1 }{ 3 }~ z&~=~0\end{array}$$	15
94	Solve system of equations using Elimination method $$\begin{array}{ cccc }5~ x&+~~10~ y&+~~30~ z&~=~12.9\\10~ x&+~~30~ y&+~~100~ z&~=~37.1\\30~ x&+~~100~ y&+~~354~ z&~=~130.3\end{array}$$	15
95	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~9~ y&+~~~~ z&~=~20\\~~ x&+~~10~ y&-~~~2~ z&~=~18\\3~ x&+~~27~ y&+~~2~ z&~=~58\end{array}$$	14
96	Solve system of equations using Elimination method $$\begin{array}{ cccc }4~ x&+~~3~ y&+~~2~ z&~=~95\\5~ x&+~~2~ y&+~~3~ z&~=~98\\12~ x&+~~9~ y&+~~6~ z&~=~278\end{array}$$	14
97	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&+~~2~ y&-~~~~~ z&~=~-3\\2~ x&-~~~~~ y&+~~~~ z&~=~5\\~~ x&-~~~~~ y&+~~~~ z&~=~4\end{array}$$	14
98	Solve system of equations using Elimination method $$\begin{array}{ cccc }~~ x&-~~~~~ y&+~~3~ z&~=~2\\2~ x&+~~3~ y&-~~~~~ z&~=~5\\-1~ x&-~~~9~ y&+~~11~ z&~=~-4\end{array}$$	14
99	Solve system of equations using Elimination method $$\begin{array}{ cccc }14~ x&+~~22~ y&+~~40~ z&~=~780\\~~ x&+~~~~ y&+~~~~ z&~=~40\\&-~~~2~ y&+~~~~ z&~=~-10\end{array}$$	14
100	Solve system of equations using Elimination method $$\begin{array}{ cccc }7~ x&+~~4~ y&+~~2~ z&~=~24\\5~ x&+~~3~ y&+~~6~ z&~=~30\\3~ x&+~~7~ y&+~~10~ z&~=~46\end{array}$$	14