Determine the number of solutions to the system of linear equations. Y = x + 5 and y = -x + 5 is the answer 1, infinite, 2 or 0?
The given system of linear equations is:
Y = x + 5 ...(1)
y = -x + 5 ...(2)
To determine the number of solutions, we can compare the slopes of the two equations.
The equation (1) is in the form Y = mx + b, where m is the slope. So, the slope of equation (1) is 1.
The equation (2) is also in the form y = mx + b, where m is the slope. So, the slope of equation (2) is -1.
Since the slopes of the two equations are different, this means that the lines represented by the equations are not parallel.
If two lines are not parallel, they must intersect at exactly one point. Therefore, the system of linear equations has 1 solution.
Hence, the answer is 1.
Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is the statement true or false? Explain
The given system of linear equations is:
y = -x + 3 ...(1)
x + y = 8 ...(2)
To determine the number of solutions, we can graph the equations and see where they intersect.
First, let's rearrange equation (2) to isolate y:
x + y = 8
y = 8 - x ...(3)
Now we have the equations (1) and (3), which represent two lines.
Equation (1) has a y-intercept of 3 and a slope of -1. This means that it moves 1 unit down for every 1 unit it moves to the right.
Equation (3) has a y-intercept of 8 and a slope of -1. This means that it moves 1 unit down for every 1 unit it moves to the right.
Now let's graph the two lines:
Graph of equation (1):
y = -x + 3
Here, the y-intercept is 3, so plot a point at (0, 3). Then use the slope of -1 to find additional points. Move 1 unit to the right, then 1 unit down, and plot another point at (1, 2). Continue this pattern to draw the line.
Graph of equation (3):
y = 8 - x
Here, the y-intercept is 8, so plot a point at (0, 8). Then use the slope of -1 to find additional points. Move 1 unit to the right, then 1 unit down, and plot another point at (1, 7). Continue this pattern to draw the line.
Upon graphing the two lines, we can observe that they are parallel and do not intersect. This means that there is no point that satisfies both equations simultaneously.
Hence, the statement is true.
Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. Is the statement true or false? Explain
A. The statement is false because the lines have an intersection point
B. The statement is true because the lines have an intersection point
C. The statement is true because the lines are parallel
D. The statement is false because the lines are parallel
C. The statement is true because the lines are parallel.
Upon graphing the two lines, we can observe that they are parallel and do not intersect. This means that there is no point that satisfies both equations simultaneously.
Therefore, the statement is true because the lines have no intersection point.
Does the graph show the system of equations x + y = 2 and -x + y = 7. Should the lines for the system be parallel? A. The graph of x plus y equals 2 is incorrect. The line should intersect. B. Both graphs are correct. The lines should be parallel. C. The graph of -x + y = 7 is incorrect. The lines should intersect. D. The graph of negative x + y = 7 is incorrect. The lines should be parallel
D. The graph of negative x + y = 7 is incorrect. The lines should be parallel.
The given system of equations is:
x + y = 2 ...(1)
-x + y = 7 ...(2)
To determine the correctness of the graph, we need to analyze the slopes of the lines represented by the equations.
Equation (1) can be rearranged to isolate y:
y = 2 - x ...(3)
Equation (2) can also be rearranged to isolate y:
y = 7 + x ...(4)
In equation (3), we see that the coefficient of x is -1, which means the slope of the line is -1.
In equation (4), we see that the coefficient of x is 1, meaning the slope of the line is 1.
Since the slopes of the lines are different (-1 and 1), this implies that the lines should be parallel, not intersecting.
Therefore, the graph incorrectly shows the lines intersecting when they should be parallel. Hence, option D is the correct answer.
If it's 1:36am how long will it be til 2:30am
If it is currently 1:36 am, and you are asking how long it will be until 2:30 am, you can calculate the time difference by subtracting the current time from the target time.
To calculate the time difference, we need to convert both times to a standard format (such as 24-hour format) for an accurate calculation.
In 24-hour format, 2:30 am is represented as 02:30.
To calculate the time difference:
02:30 - 01:36
First, subtract the minutes:
30 - 36 = -6
Then, subtract the hours and adjust if necessary:
02 - 01 = 1
Since the result of subtracting the minutes is negative, we need to borrow 60 minutes from the hours:
-6 + 60 = 54
Now, we have our time difference: 1 hour and 54 minutes.
Therefore, it will be 1 hour and 54 minutes until 2:30 am if it is currently 1:36 am.