Answer: old McDonald has 54 chickens and 2 cows.
Step-by-step explanation:
Let x represent the number of chickens that old McDonald have.
Let y represent the number of cows that old McDonald have.
He counted 56 heads. A chicken and a cow has one head each. It means that
x + y = 56
He counted 116 legs. A chicken has 2 legs and a cow has 4 legs. It means that
2x + 4y = 116 - - - - - - - - -1
Substituting x = 56 - y into equation 1, it becomes
2(56 - y) + 4y = 116
112 - 2y + 4y = 116
- 2y + 4y = 116 - 112
2y = 4
y = 4/2 = 2
x = 56 - y = 56 - 2
x = 54
Answer:
C
Step-by-step explanation:
sin C=12/13
cos A=12/13
so sin C=cos A
Answer:
<h2>
The solution to the system of equation is x = 8, y = 13</h2>
Step-by-step explanation:
The system of equation using matrix equation can be solved using crammers rule. Given the equation;
7x-4y=4
10x-6y=2
The equation will be rewritten in the format AX = B
matrix A will be 2*2 matrix
X will be a column matrix containing the variables
B will be a column matrix
![\left[\begin{array}{cc}7&-4\\10&-6\\\end{array}\right] \left[\begin{array}{c}x&y\\\\\end{array}\right] = \right] \left[\begin{array}{c}4&2\\\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%26-4%5C%5C10%26-6%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%262%5C%5C%5C%5C%5Cend%7Barray%7D%5Cright%5D)
first we will find the determinant of the matrix A

To get the value of x, we will substitute the column matrix at the right hand side to replace the first column pf matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.
![|X|=\left[\begin{array}{cc}4&-4\\2&-6\\\end{array}\right]\\|X|= -24+8\\|X|=-16](https://tex.z-dn.net/?f=%7CX%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-4%5C%5C2%26-6%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CX%7C%3D%20-24%2B8%5C%5C%7CX%7C%3D-16)
x = |X|/|A|
x = -16/-2
x = 8
Similarly for y, we will substitute the column matrix at the right hand side to replace the second column of matrix A, then we look for the determinant and divide the determinant by the determinant of matrix A itself.
![|Y|=\left[\begin{array}{cc}7&4\\10&2\\\end{array}\right]\\|Y|= 14-40\\|Y|=-26](https://tex.z-dn.net/?f=%7CY%7C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%264%5C%5C10%262%5C%5C%5Cend%7Barray%7D%5Cright%5D%5C%5C%7CY%7C%3D%2014-40%5C%5C%7CY%7C%3D-26)
y = |Y|/|A|
y = -26/-2
y = 13
The solution to the system of equation is x = 8, y = 13