Period____. Date________________. Solving Systems of Three Equations w/ Cramer's Rule. Use Cramer's Rule to solve each s
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Systems of Three Equations w/ Cramer's Rule
Date________________ Period____
Use Cramer's Rule to solve each system. 1) −2 x − 5 y + 4z = 21 −5 x − 5 y + z = 21 −4 y − 4z = 8
2) 5 x + y − 4z = −4 −3 y − 6z = −21 − x − y − z = −6
3) −4 x − 6z = −12 −6 x − 4 y − 2z = 6 −x + 2 y + z = 9
4) 4 x − 4 y + 2z = −14 4 x + 2 y = 14 −3 y + z = −10
5) x − 3 y + z = −7 −4 x − 6z = 4 2 x + 3 y + 2z = 4
6) 6 x + 3 y − 3z = −18 6 x + y + 4z = −28 5z = −10
7) −12 x − 4 y + 4z = −21 −4z = 6 12 x + 12 y + 4z = −1
8) 4 x + 5 y = −6 10 x − 30 y + 50z = −27 4 x + 4 y + z = −6
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Worksheet by Kuta Software LLC
9) 36 x − 6 y + 6z = −1 12 x + 6z = −3 18 x − 6 y + 6z = −1
10) −2 x + y − 4z = 4 5 x − 2 y = 18 x − 5z = 17
11) −3z = 6 2 x + y − 2z = 6 −6 x − 3 y = −6
12) 6 y + 6z = −30 4 x − 6 y − 3z = 26 x + y + z = −3
13) −6 x − y + z = −7 4z = −6 4 x − 24 y + 24z = 17
14) 3 x + 6 y = −4 x + y − z = −2 9 x − 12 y + 15z = 28
15) 5 x + 5 y + 30z = 24 5 x − 5 y − 20z = −11 −4 y + 10z = 1
16) 3 x − 1 = 3z 4 = 6 y − 3z − 3 x −2 x + 6z = 10 y − 7
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Name___________________________________
Solving Systems of Three Equations w/ Cramer's Rule
Date________________ Period____
Use Cramer's Rule to solve each system. 1) −2 x − 5 y + 4z = 21 −5 x − 5 y + z = 21 −4 y − 4z = 8
2) 5 x + y − 4z = −4 −3 y − 6z = −21 − x − y − z = −6
(−1, −3, 1)
(5, −5, 6)
3) −4 x − 6z = −12 −6 x − 4 y − 2z = 6 −x + 2 y + z = 9
4) 4 x − 4 y + 2z = −14 4 x + 2 y = 14 −3 y + z = −10
(−3, 1, 4)
No solution
5) x − 3 y + z = −7 −4 x − 6z = 4 2 x + 3 y + 2z = 4
6) 6 x + 3 y − 3z = −18 6 x + y + 4z = −28 5z = −10
(−1, 2, 0)
(−3, −2, −2)
7) −12 x − 4 y + 4z = −21 −4z = 6 12 x + 12 y + 4z = −1
(
5 5 3 ,− ,− 3 4 2
8) 4 x + 5 y = −6 10 x − 30 y + 50z = −27 4 x + 4 y + z = −6
)
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( -1-
1 8 8 ,− ,− 2 5 5
)
Worksheet by Kuta Software LLC
9) 36 x − 6 y + 6z = −1 12 x + 6z = −3 18 x − 6 y + 6z = −1
(
1 1 0, − , − 3 2
10) −2 x + y − 4z = 4 5 x − 2 y = 18 x − 5z = 17
(2, −4, −3)
)
11) −3z = 6 2 x + y − 2z = 6 −6 x − 3 y = −6
12) 6 y + 6z = −30 4 x − 6 y − 3z = 26 x + y + z = −3
(2, −1, −4)
Infinitely many solutions
13) −6 x − y + z = −7 4z = −6 4 x − 24 y + 24z = 17
(
5 3 , −2, − 4 2
)
15) 5 x + 5 y + 30z = 24 5 x − 5 y − 20z = −11 −4 y + 10z = 1
(
4 1 , 1, 5 2
14) 3 x + 6 y = −4 x + y − z = −2 9 x − 12 y + 15z = 28
(
2 4 0, − , 3 3
)
16) 3 x − 1 = 3z 4 = 6 y − 3z − 3 x −2 x + 6z = 10 y − 7
)
(
1 1 0, , − 2 3
)
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Worksheet by Kuta Software LLC
