1. Determine the number of solutions to this system of linear equations:
y = x + 5
y = −x + 5
Responses:
A. 0
B. 2
C. 1
D. Infinite
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.
On a graph there's y = -x + 3, x + y = 8
Responses:
A. The statement is false, because the lines are parallel.
B. The statement is true, because the lines are parallel.
C. The statement is false, because the lines have an intersection point.
D. The statement is false, because the lines have an intersection point.
3. Does the graph show the system of equations x + y = 2 and −x + y = 7? Should the lines for the system be parallel? Note there's no graph.
Responses:
A. The statement is false, because the lines are parallel.
B. The statement is false, because the lines are parallel.
C. The statement is false, because the lines are parallel.
D. The statement is false, because the lines are parallel.
4. Which of these graphs shows that the linear system −2x + y = 6 and 4x − 2y = −12 has an infinite number of solutions?
Responses:
A. A graph with two slopes one that starts at (-8, -10) and ends at (2, 10) and one that starts at (-5, -10) and ends at (5, 10).
B. A graph with a slope that starts at (-8, -10) and ends at (2, 10).
C. A graph with two slopes one that starts at (-4, -10) and ends at (4, 10).
D. A graph with a slope that starts at (-2, -10) and ends at (8, 10).
5. Which of these graphs shows that the linear system y = −x + 6 and 3x + 3y = 18 has an infinite number of solutions?
Responses:
A. A graph with a slope that starts at (4, 10) on the x axis and ends on (4, 10) on the y axis.
B. A graph with two slopes one that starts at (6, 10) on the x axis and ends at (7, 10) on the y axis and one that starts on (5, 10) on the x axis and ends at (5, 10) on the y axis.
C. A graph with two slopes one that starts at (4, 10) on the y axis and ends at (3, 10) on the x axis and one that starts on (5, 10) on the x axis and ends at (5, 10) on the y axis.
D. A graph with a slope that starts at (5, 10) on the x axis and ends on (5, 10) on the y axis.
1. C. 1
2. C. The statement is false, because the lines have an intersection point.
3. D. The statement is false, because the lines are parallel.
4. B. A graph with a slope that starts at (-8, -10) and ends at (2, 10).
5. D. A graph with a slope that starts at (5, 10) on the x axis and ends on (5, 10) on the y axis.