10. Represent the system of equations in augmented matrix form.
y = (Image: three-fourths)x – 6
y =–8x + 2
| 3/4 | -1 || y |
| -8 | 1 || 2 |
10. Represent the system of equations in augmented matrix form.
y = (Image: three-fourths)x – 6
y =–8x + 2
| 3/4 | -1 || y |
| -8 | 1 || 2 |
To represent the system of equations in augmented matrix form, we need to convert the equations into a matrix format.
The augmented matrix is a way to represent a system of linear equations by organizing the coefficients of the variables and the constants into a matrix.
Let's start with the given equations:
Equation 1: y = (3/4)x - 6
Equation 2: y = -8x + 2
To represent these equations in augmented matrix form, we need to rearrange them in a specific format:
First, we'll group the coefficients of the variables (x and y) on one side of the equations, and the constants on the other side:
Equation 1: (3/4)x - y = -6
Equation 2: 8x + y = 2
Now, we can write the coefficients of x, y, and the constants in matrix form:
| 3/4 -1 | -6 |
| 8 1 | 2 |
In this augmented matrix, the left side represents the coefficients of the variables (x and y), and the right side represents the constants.
So, the augmented matrix form for the given system of equations is:
| 3/4 -1 | -6 |
| 8 1 | 2 |