Using Cramer’s Rule to Solve Two Equations With Two Unknowns
Practice Problems
1.
Use Cramer’s Rule to solve:
2.
Use Cramer’s Rule to solve:
3.
Use Cramer’s Rule to solve:
4.
Use Cramer’s Rule to solve:
5.
Use Cramer’s Rule to solve:
Answers
1.
(–2, –3)
2.
(
3.
(–2, 1)
4.
(
5.
(
)
)
)
Using Cramer’s Rule to Solve Two Equations With Two Unknowns – Practice
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Detailed Solutions
1.
Use Cramer’s Rule to solve:
Step 1: Find the determinant, D, by using the x and y values from the problem.
–20
|
(
|
)
–9
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y column unchanged.
4
|
|
–18
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x column unchanged.
30
|
|
–3
Step 4: Use Cramer’s Rule to find the values of x and y.
The answer written as an ordered pair is (–2, –3).
2.
Use Cramer’s Rule to solve:
Step 1: Find the determinant, D, by using the x and y values from the problem.
–12
|
|
(
)
42
Using Cramer’s Rule to Solve Two Equations With Two Unknowns – Practice
Page 2 of 5
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y column unchanged.
18
|
|
77
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x column unchanged.
44
|
|
–36
Step 4: Use Cramer’s Rule to find the values of x and y.
The answer written as an ordered pair is (
3.
).
Use Cramer’s Rule to solve:
Step 1: Find the determinant, D, by using the x and y values from the problem.
15
|
|
–8
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y column unchanged.
–10
|
|
(
)
36
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x column unchanged.
27
|
|
4
Using Cramer’s Rule to Solve Two Equations With Two Unknowns – Practice
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Step 4: Use Cramer’s Rule to find the values of x and y.
The answer written as an ordered pair is (–2, 1).
4.
Use Cramer’s Rule to solve:
Step 1: Find the determinant, D, by using the x and y values from the problem.
45
|
|
48
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y column unchanged.
–18
|
|
(
)
–56
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x column unchanged.
–35
|
|
(
)
–12
Step 4: Use Cramer’s Rule to find the values of x and y.
The answer written as an ordered pair is (
).
Using Cramer’s Rule to Solve Two Equations With Two Unknowns – Practice
Page 4 of 5
5.
Use Cramer’s Rule to solve:
Step 1: Find the determinant, D, by using the x and y values from the problem.
–14
|
(
|
)
–36
Step 2: Find the determinant, Dx, by replacing the x-values in the first column with the values
after the equal sign leaving the y column unchanged.
49
|
|
–144
Step 3: Find the determinant, Dy, by replacing the y-values in the second column with the
values after the equal sign leaving the x column unchanged.
–35
|
|
–12
Step 4: Use Cramer’s Rule to find the values of x and y.
The answer written as an ordered pair is (
).
Using Cramer’s Rule to Solve Two Equations With Two Unknowns – Practice
Page 5 of 5