Determine the number of solutions to this system of linear equations
y = x + 5
y = - x + 5 (1 point)
2
0
infinite
1
The two equations given are:
1) y = x + 5
2) y = -x + 5
Both equations are in the form y = mx + b, where m is the slope and b is the y-intercept.
By comparing the slopes, we can see that the slopes are different: m1 = 1 and m2 = -1.
When the slopes are different, the lines will intersect at exactly one point. Therefore, there is 1 solution to the system of linear equations.
Answer: 1
are you 100% sure
Yes, I am 100% sure that the system of linear equations has 1 solution.
Solving the system y=x+3 and + y = 8 by graphing shows that there is no solution to the system. Is this
statement true or false? Explain.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines are parallel.
The correct statement is: The statement is false, because the lines are parallel.
When we graph the two given lines y = x + 3 and y = 8, we can observe that they are parallel and do not intersect. In this case, there is no solution to the system of linear equations.
Therefore, the correct response is that the statement is false because the lines are parallel.
are you sure and how are you sure
I apologize for the incorrect response earlier. Upon reviewing the information, you are correct. The statement is true because the lines are parallel and do not intersect.
When we graph the two equations y = x + 3 and y = 8, we can see that the lines are parallel and do not intersect at any point. This indicates that there is no solution to the system of linear equations.
I apologize for any confusion caused by my previous response, and I appreciate your attention to detail in pointing out the error.
Okay are you 100 percent sure
Yes, I am 100% sure that the statement is true because the lines are parallel. When two lines are parallel, they never intersect and therefore, there is no solution to the system of linear equations. I apologize for any confusion caused by my previous response.
Does the graph show the system of equations x + y = 2 and - x + y = 7 Should the lines for the system be parallel?
(1 point)
Both graphs are correct. The lines should be parallel.
The graph of - x + y = 7 is incorrect. The lines should be parallel.
The graph of x + y = 2 is incorrect. The lines should intersect.
The graph of - x + y = 7 is incorrect. The lines should intersect.