Answer: The determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
Step-by-step explanation: The given system of linear equations is :
We are given to find the determinant of the coefficient matrix and to find the values of x, y and z.
The determinant of the co-efficient matrix is given by
Now, from equations (ii) and (iii), we have
Substituting the value of y and z from equations (iv) and (v) in equation (i), we get
From equations (iv) and (v), we get
Thus, the determinant of the coefficient matrix is -15 and x = 3, y = 4, z = 1.
Answer:
x=5 and y=16
Step-by-step explanation:
x = number of pants
y = number of shirts
Set up equations:
- 25x + 14.5y = 357
- x + y = 21
Set the equations up as a system:
25x+14.5y=357
x+y=21
Steps:
Solve the system by substitution.
(You can also solve this system by elimination.)
<em>25x + 14.5y= 357</em>
<em>x + y = 21</em>
Step 1: Solve x+y=21 for x:
(x + y) − y = (21) − y(Subtract y from both sides)
x = −y + 21
Step 2: Substitute −y + 21 for x in 25x + 14.5y = 357:
25x + 14.5y = 357
25(−y + 21) + 14.5y = 357
−10.5y + 525 = 357 (Simplify both sides of the equation)
(−10.5y + 525) − 525 = (357) − 525(Subtract 525 to both sides)
−10.5y = −168
−10.5y / −10.5 = −168 / −10.5 (Divide both sides by -10.5)
y = 16
Step 3: Substitute 16 for y in x = −y + 21:
x = −y + 21
x = −16 + 21
x = 5 (Simplify both sides of the equation)
Answer:
x=5 and y=16
N = -11. If 4 less than n is -15, then the following must be true.
Answer:
Answer:
A. 2 sinx cosx - 1 + 2 sin^2 x.
Step-by-step explanation:
sin2x = 2 sinx cosx
cos2x = cos^2x - sin^2x
So sin2x - cos2x = 2 sinx cosx - ( cos^2x - sin^2x)
But cos^2 x = 1 - sin^2 x, so we have:
2 sinx cosx - (1 - sin^2 x - sin^2x)
= 2 sinx cosx - 1 + 2 sin^2 x.
