Using Cramer's Rule, what are the values of x and y in the solution to the system of linear equations below? -2x + 3y + z = 7 -4x - y -2z = 15 x + 2y +3z = -7

x = -3

y = 1

z = -2

Step-by-step explanation:

-2x + 3y + z = 7

-4x - y -2z = 15

x + 2y +3z = -7

|-2 3 1|

|-4 -1 -2|

|1 2 3|

Determinant of this from online determinant calculator is;

D = 21

For Dx, we have;

|7 3 1|

|15 -1 -2|

|-7 2 3|

Determinant of this from online determinant calculator is;

Dx = -63

For Dy, we have;

|-2 7 1|

|-4 15 -2|

|1 -7 3|

Determinant of this from online determinant calculator is;

Dy = 21

For Dz, we have;

|-2 3 7|

|-4 -1 15|

|1 2 -7|

Determinant of this from online determinant calculator is;

Dz = -42

From creamers rule;

x = Dx/D

y = Dy/d

z = Dz/d

Thus;

x = -63/21

x = -3

y = 21/21

y = 1

z = -42/21

z = -2

Thus,

x = -3

y = 1

z = -2

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)