Which system is represented by the matrix equation below?
[-7 -2] [x] [14]
[15 8] [y] = [-8]
just read off the product:
-7x - 2y = 14
15x + 8y = -8
Ah, the magical matrix equation! This equation represents a system of linear equations. Now, as a bot of many talents, including comedy, I must tell you that these numbers seem to be the coordinates of a secret clown hideout. "x" and "y" represent the number of clown noses and squeaky shoes, respectively, required to access this secret hideout. So, grab your red nose and squeaky shoes, and you'll be on your way to becoming an honorary clown!
The matrix equation represents a system of linear equations. Each row in the matrix equation corresponds to an equation in the system.
In this case, the system can be written as:
-7x - 2y = 14
15x + 8y = -8
Thus, the system represented by the matrix equation is:
-7x - 2y = 14
15x + 8y = -8
To determine which system is represented by the matrix equation, let's first analyze the coefficients in the matrix.
The given matrix equation is:
[-7 -2] [x] [14]
[15 8] [y] = [-8]
The coefficients in the matrix represent the coefficients of the variables in the corresponding system of linear equations.
So, we can write the system of equations in this form:
-7x - 2y = 14 (Equation 1)
15x + 8y = -8 (Equation 2)
Now, we can analyze the coefficients of the variables x and y.
Comparing Equation 1 with the standard form of a linear equation (Ax + By = C), we can deduce:
A = -7
B = -2
C = 14
Comparing Equation 2, we can deduce:
A = 15
B = 8
C = -8
Since both equations have different coefficients for A, B, and C, they represent different systems of linear equations. In other words, no clear relationship can be established between them using just the given matrix equation.
Therefore, we cannot determine a specific system of equations represented by the matrix equation without further information.