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 have an intersection point. The statement is true, because the lines have an intersection point. The statement is true, because the lines are parallel. The statement is true, because the lines are parallel. The statement is false, because the lines have an intersection point. The statement is false, because the lines have an intersection point. The statement is false, because the lines are parallel.
The statement is false, because the lines have an intersection point.
To solve the system of equations y = -x + 3 and x + y = 8, we can graph the two lines and see if they intersect at a point.
The equation y = -x + 3 represents a line with a slope of -1 and a y-intercept of 3. The equation x + y = 8 can be rewritten as y = -x + 8, which represents a line with a slope of -1 and a y-intercept of 8.
Both lines have the same slope, -1, which means they are not parallel. And if two lines are not parallel, they must intersect at a point.
Therefore, the statement is false, as there is an intersection point between the lines.
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) Responses Both graphs are correct. The lines should be parallel. 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 negative x plus y equals 7 is incorrect. The lines should be parallel. The graph of x+y=2 is incorrect. The lines should intersect. The graph of x plus y equals 2 is incorrect. The lines should intersect. The graph of −x+y=7 is incorrect. The lines should intersect.
The graph does not show the system of equations x+y=2 and −x+y=7. The lines for the system should not be parallel.
To solve the system of equations x+y=2 and −x+y=7, we can rewrite the equations in slope-intercept form to determine their slopes and y-intercepts.
The equation x+y=2 can be rewritten as y = -x + 2, which has a slope of -1 and a y-intercept of 2.
The equation −x+y=7 can be rewritten as y = x + 7, which has a slope of 1 and a y-intercept of 7.
Since the slopes of the lines are different, they are not parallel. Additionally, since the slopes are not equal, the two lines intersect at a single point.
Therefore, the correct response is: The graph of x+y=2 is incorrect. The lines should intersect.
Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point)
To determine which graph shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions, we need to analyze the slopes and intercepts of the lines represented by each equation.
For the equation −2x+y=6, we can rewrite it in slope-intercept form as y = 2x + 6. This line has a slope of 2 and a y-intercept of 6.
For the equation 4x−2y=−12, we can rewrite it in slope-intercept form as y = 2x + 6. This line also has a slope of 2 and a y-intercept of 6.
Since both equations have the same slope and the same y-intercept, they represent the same line. This means that the two lines are coincident or overlapping, and therefore the system has an infinite number of solutions.
Therefore, the correct option is: Both graphs.
There's only four pick 1
Apologies for the confusion. The correct answer is: All graphs show that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions.
Which of these graphs shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions?(1 point)
To determine which graph shows that the linear system y = -x + 6 and 3x + 3y = 18 has an infinite number of solutions, we need to analyze the slopes and intercepts of the lines represented by each equation.
For the equation y = -x + 6, we can see that it has a slope of -1 and a y-intercept of 6.
For the equation 3x + 3y = 18, we can rearrange it as y = -x + 6. Here we can see that it also has a slope of -1 and a y-intercept of 6.
Since both equations have the same slope and the same y-intercept, they represent the same line. This means that the two lines are coincident or overlapping, and therefore the system has an infinite number of solutions.
Therefore, the correct answer is: All graphs.