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.
y=−3x+5
2y=−6x+10
19 answers
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
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).
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).
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).
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).
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).
so these lines should be parallel and not intersect
Apologies for the incorrect response. No, these lines are not parallel.
The given system of linear equations is:
x + y = 2
-x + y = 7
By rearranging the equations to slope-intercept form, we have:
y = -x + 2 ------> (1)
y = x + 7 ------> (2)
Comparing the slopes, we see that the coefficient of x in equation (1) is -1, and the coefficient of x in equation (2) is 1.
Since the slopes are different (-1 and 1), the lines are not parallel. Therefore, they will intersect at a single point.
Therefore, the correct answer is 1 (one solution).
The given system of linear equations is:
x + y = 2
-x + y = 7
By rearranging the equations to slope-intercept form, we have:
y = -x + 2 ------> (1)
y = x + 7 ------> (2)
Comparing the slopes, we see that the coefficient of x in equation (1) is -1, and the coefficient of x in equation (2) is 1.
Since the slopes are different (-1 and 1), the lines are not parallel. Therefore, they will intersect at a single point.
Therefore, the correct answer is 1 (one solution).
so which of these responses would it be
The graph of x+y=2 is incorrect. The lines should intersect.
The graph of −x+y=7 is incorrect. The lines should intersect.
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.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=7 is incorrect. The lines should be parallel.
I apologize for the confusion.
Given the system of linear equations:
x + y = 2
-x + y = 7
Upon comparing the equations, we can see that they have different slopes, which implies that they are not parallel. Therefore, the lines should intersect at a single point.
However, from the given responses, none of them accurately reflect this information.
The correct response should be:
None of the above responses accurately describe the situation. The lines should intersect.
Given the system of linear equations:
x + y = 2
-x + y = 7
Upon comparing the equations, we can see that they have different slopes, which implies that they are not parallel. Therefore, the lines should intersect at a single point.
However, from the given responses, none of them accurately reflect this information.
The correct response should be:
None of the above responses accurately describe the situation. The lines should intersect.
Solve the given system of linear equations by inspection.
y=3/5x−5
y=−3/5x−5
(1 point)
Responses
infinitely many solutions
no solution
(0,−5)
(−5,0)
y=3/5x−5
y=−3/5x−5
(1 point)
Responses
infinitely many solutions
no solution
(0,−5)
(−5,0)
To solve the given system of linear equations by inspection, we can equate the two equations since they are both equal to y:
3/5x - 5 = -3/5x - 5
By simplifying the equation, we get:
3/5x + 3/5x = 0
Combining the terms, we have:
(3/5 + 3/5)x = 0
Simplifying further:
(6/5)x = 0
To solve for x, we can multiply both sides by the reciprocal of 6/5:
(x * 5/6) * (6/5) = 0 * (6/5)
x = 0
Now, we can substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
y = 3/5 * 0 - 5
y = -5
Therefore, the solution to the given system of linear equations is (x, y) = (0, -5).
The correct response is: (0, -5)
3/5x - 5 = -3/5x - 5
By simplifying the equation, we get:
3/5x + 3/5x = 0
Combining the terms, we have:
(3/5 + 3/5)x = 0
Simplifying further:
(6/5)x = 0
To solve for x, we can multiply both sides by the reciprocal of 6/5:
(x * 5/6) * (6/5) = 0 * (6/5)
x = 0
Now, we can substitute the value of x back into either of the original equations to solve for y. Let's use the first equation:
y = 3/5 * 0 - 5
y = -5
Therefore, the solution to the given system of linear equations is (x, y) = (0, -5).
The correct response is: (0, -5)
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
(1 point)
Responses
The statement is true, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
To determine if the statement is true or false, we need to analyze the given system of linear equations:
y = -x + 3
x + y = 8
By graphing these equations, we can visually check whether or not they intersect.
The first equation, y = -x + 3, has a slope of -1 and a y-intercept of 3. This means it is a straight line that goes downward from left to right.
The second equation, x + y = 8, can be rewritten as y = -x + 8. It also has a slope of -1 but a y-intercept of 8. This line also goes downward from left to right.
When we graph these lines, we see that they intersect at the point (2, 6).
Therefore, the statement "Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system" is FALSE.
The correct response is: The statement is false because the lines have an intersection point.
y = -x + 3
x + y = 8
By graphing these equations, we can visually check whether or not they intersect.
The first equation, y = -x + 3, has a slope of -1 and a y-intercept of 3. This means it is a straight line that goes downward from left to right.
The second equation, x + y = 8, can be rewritten as y = -x + 8. It also has a slope of -1 but a y-intercept of 8. This line also goes downward from left to right.
When we graph these lines, we see that they intersect at the point (2, 6).
Therefore, the statement "Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system" is FALSE.
The correct response is: The statement is false because the lines have an intersection point.
but when its been declared as no solution they will not right intersect
Apologies for the confusion.
To determine if the statement is true or false, we need to analyze the given system of linear equations:
y = -x + 3
x + y = 8
By rearranging the second equation, we have:
y = 8 - x
Comparing the coefficients of x, we see that the equations have different slopes (-1 and -1/1).
When graphed, these lines are not parallel and will intersect at a point.
Therefore, the statement "Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system" is FALSE.
The correct response is: The statement is false because the lines have an intersection point.
To determine if the statement is true or false, we need to analyze the given system of linear equations:
y = -x + 3
x + y = 8
By rearranging the second equation, we have:
y = 8 - x
Comparing the coefficients of x, we see that the equations have different slopes (-1 and -1/1).
When graphed, these lines are not parallel and will intersect at a point.
Therefore, the statement "Solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system" is FALSE.
The correct response is: The statement is false because the lines have an intersection point.