Answer:
To determine the classification of each system, let's analyze the equations provided.
The first system of equations is:
x + 5y = -2
x + 5y = 4
In this system, both equations have the same coefficients for x and y. When we subtract the second equation from the first equation, we get:
0 = -6
This indicates that the system has no solution. The lines representing these equations are parallel and will never intersect. Therefore, the classification of this system is "inconsistent."
The second system of equations is:
y = 3x + 4
-2x + y = 4
In this system, the first equation represents a linear equation in slope-intercept form. The coefficient of x is 3, which represents the slope of the line, and the constant term 4 represents the y-intercept.
The second equation can be rearranged to y = 2x + 4. This equation is also in slope-intercept form, with a slope of 2 and a y-intercept of 4.
Since both equations have different slopes and different y-intercepts, the lines representing these equations will intersect at a single point. Therefore, the classification of this system is "consistent and independent."
The third system of equations is:
3x + y = 4
-6x - 2y = -8
To analyze this system, we can manipulate the second equation by dividing it by -2, which gives us 3x + y = 4.
We can see that the two equations are equivalent, representing the same line. Every point on the line will satisfy both equations. Therefore, the classification of this system is "consistent and dependent."
In summary, the classifications of the given systems are:
- The first system is "inconsistent."
- The second system is "consistent and independent."
- The third system is "consistent and dependent."
Explanation: