One Solution No Solution Or Many Solutions Quick Check
1. Determine the number of solutions to this system of linear equations.
y = x + 5
y = -x + 5
One solution
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.
A. The statement is true, because the lines have an intersection point.
B. The statement is false, because the lines are parallel.
C. The statement is false, because the lines have an intersection point.
D. The statement is true, because the lines are parallel.
C. The statement is false, because the lines have an intersection point.
Explanation: If the lines have an intersection point, then there is a solution to the system of equations. In this case, since the lines do intersect, there is a solution.