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 false, because the lines have an intersection point. 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 true, because the lines have an intersection point. The statement is false, because the lines are parallel. The statement is false, because the lines are parallel. The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
By graphing the system of equations y=−x+3 and x+y=8, we can observe that the lines never intersect. This means that there are no solutions to the system of equations. Therefore, 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 this statement true or false? Explain. (1 point) Responses 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 true, 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 statement is false, 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.
By graphing the system of equations y=−x+3 and x+y=8, we can see that the lines do indeed intersect at the point (2,6). Therefore, there is a solution to the system of equations.
etermine the number of solutions to this system of linear equations: y=x+5 y=−x+5 (1 point) Responses
The number of solutions to this system of linear equations is 1.
By graphing the equations y=x+5 and y=−x+5, we can see that the lines intersect at the point (0,5). This means that there is a single solution to the system of equations.
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 The graph of −x+y=7 is incorrect. The lines should intersect. The graph of negative x plus y equals 7 is incorrect. The lines should intersect. 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+y=2 is incorrect. The lines should intersect.
If we graph the equations x+y=2 and −x+y=7, we can see that the lines do not appear to intersect. Therefore, the graph is incorrect. The correct graph should show that the lines intersect.