Which of the following statements describe the system?
{y = 3x + 2
{y = −2x − 1
Select two answers.
A. consistent**
B. inconsistent
C. infinite solutions**
D. one solution
Am I right??????
A. consistent
D. one solution
Try to solve this system.
Solution is : x = - 3 / 5 , y = 1 / 5
Correct
Well, you could say that the system is "consistent" because it has solutions. But you would only be partially right. There is something else you're missing, my friend. The system is not just consistent; it actually has "infinite solutions"! So, your correct answers are "A. consistent" and "C. infinite solutions." Keep up the good work!
Yes, you are correct. The statements describe a system of linear equations. A system of equations can be classified based on the number of solutions it has.
In this case, the system consists of two equations:
1. y = 3x + 2
2. y = -2x - 1
Given these equations, we can determine the classification of the system.
To find the classifications:
1) Solve the system of equations to find if there is one solution, infinite solutions, or no solution.
2) Determine if the system is consistent (has solutions) or inconsistent (has no solution).
To solve the system, we can set these equations equal to each other:
3x + 2 = -2x - 1
Combining like terms, we have:
5x = -3
Dividing both sides by 5, we find:
x = -3/5
Substituting this value of x back into one of the equations, let's use the first equation y = 3x + 2:
y = 3(-3/5) + 2
y = -9/5 + 2
y = -9/5 + 10/5
y = 1/5
So the values of x = -3/5 and y = 1/5 satisfy both equations, which means there is one solution.
Therefore, the correct classifications for this system are:
A. consistent - there is at least one solution (in this case, exactly one solution)
C. infinite solutions - there are no infinite solutions (in this case, exactly one solution)
So your answer is correct. Well done!
Yes, you are correct! To determine the nature of the system of equations, we need to compare the slopes and y-intercepts of the two equations.
The given equations are:
1) y = 3x + 2
2) y = -2x - 1
By comparing the coefficients of x in both equations, we can see that the slopes are different. The first equation has a slope of 3, while the second equation has a slope of -2.
Since the slopes are different, the system of equations represents two lines that are not parallel or coincident. Therefore, the system is inconsistent.
Now let's check the y-intercepts of the two equations:
1) y = 3x + 2
2) y = -2x - 1
The y-intercept of the first equation is 2, and the y-intercept of the second equation is -1.
Since the y-intercepts are different, the lines will intersect at a single point. Therefore, the system has one solution.
So, the correct answers are A. consistent and D. one solution.