solve equation by cramers rule 3x+4y=-14-2x-3y=11
Answers
Answer:
2x + 3y − z = 1
4x + y − 3z = 11
3x − 2y + 5z = 21
.
Step 1: Find the determinant, D, by using the x, y, and z values from the problem.
−3 12 60
D = |
2 3 −1
4 1 −3
3 −2 5
| = |
2 3 −1
4 1 −3
3 −2 5
|
2 3
4 1
3 −2
= −9 − 69 = −78
10 −27 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 and z columns unchanged.
−21 6 165
Dx = |
1 3 −1
11 1 −3
21 −2 5
| = |
1 3 −1
11 1 −3
21 −2 5
|
1 3
11 1
21 −2
= −162 − 150 = −312
5 −189 22
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 and z columns unchanged.
−33 −126 20
Dy = |
2 1 −1
4 11 −3
3 21 5
| = |
2 1 −1
4 11 −3
3 21 5
|
2 1
4 11
3 21
= 17 − (−139) = 156
110 −9 −84
Step 4: Find the determinant, Dz, by replacing the z-values in the third column with the values
after the equal sign leaving the x and y columns unchanged.
3 −44 252
Dz = |
2 3 1
4 1 11
3 −2 21
| = |
2 3 1
4 1 11
3 −2 21
|
2 3
4 1
3 −2
= 133 − 211 = −78
42 99 −8
Step 5: Use Cramer’s Rule to find the values of x, y, and z.
x =
Dx
D
=
−312
−78 = 4
y =
Dy
D
=
156
−78 = −2
z =
Dz
D
=
−78
−78 = 1
Generally, the answer is written as on order triple (4, –2, 1) representing the x, y, and z values
Step-by-step explanation: