Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.
y=−3x+5
2y=−6x+10
The given system of linear equations is:
y = -3x + 5
2y = -6x + 10
By inspection, we can see that the second equation is simply the first equation multiplied by 2. Therefore, both equations represent the same line.
Since the two equations represent the same line, there are infinitely many solutions to the system of linear equations.
Therefore, the correct answer is: 3 (infinitely many solutions).
Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.
2x−7y=4
2x−7y=−4
The given system of linear equations is:
2x - 7y = 4
2x - 7y = -4
By inspection, we can see that the two equations are identical.
When this happens, it means that the system has infinitely many solutions.
Therefore, the correct answer is: 3 (infinitely many solutions).
its actually no solution
Apologies for the confusion. You are correct.
The given system of linear equations is:
2x - 7y = 4
2x - 7y = -4
By inspection, we can see that the coefficients of x and y are the same in both equations, but the constant terms on the right side are different.
Since the equations represent parallel lines with the same slope but different y-intercepts, there is no point where the two lines intersect.
Therefore, the correct answer is: 2 (no solution).
question how do you check the lines to make sure they are parallel or not
To check if two lines are parallel or not, you need to compare their slopes.
In the given system of linear equations:
2x - 7y = 4
2x - 7y = -4
The equations are in the form y = mx + b, where m represents the slope.
Comparing the coefficients of x, we can see that both equations have a slope of 2/7 in this case.
Since the slopes of the two lines are the same, the lines are parallel.
Therefore, the correct answer is: 3 (infinitely many solutions).
how do you check x+y=2 and -x+y=7 how can u check to see if these lines are parallel or not
To determine if two lines are parallel, you need to compare their slopes.
In this case, the given system of linear equations is:
x + y = 2
-x + y = 7
To compare the slopes of the lines, we need to transform the equations into slope-intercept form (y = mx + b), where m represents the slope.
For the first equation, x + y = 2, we can subtract x from both sides to isolate y:
y = -x + 2
For the second equation, -x + y = 7, we can add x to both sides:
y = x + 7
By comparing the two equations, we can see that they have different slopes. The first equation has a slope of -1, while the second equation has a slope of 1.
Since the slopes of the lines are different, the lines are not parallel.
Therefore, the correct answer is: 1 (one solution).