Determine the number of solutions to this system of linear equations: y=x+5 y=−x+5(1 point)

Question

A.infinite
B.0
C.1
D.2

Answer 1

C. 1

Answer 2

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.

Answer 3

The statement is false, because the lines have an intersection point.

If you plot the equations y=−x+3 and x+y=8, you will see that they intersect at the point (5, 3). This means that there is a solution to the system of equations.

Answer 4

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.

Answer 5

The graph of -x+y=7 is incorrect. The lines should intersect.

For the system of equations x+y=2 and -x+y=7, the lines are not parallel because they have different slopes (-1 and +1). The correct graph should show that the lines intersect at the solution point.