A system of three equations is graphed in the xy-plane above. How many solutions does the system have?

Options

A. None
B. One
C. Two
D. Three

Answer

B

Explanation

A solution to the system of three equations is any ordered pair (x, y) that is a solution to each of the three equations. Such an ordered pair (x, y) must lie on the graph of each equation in the xy-plane, in other words, it must be a point where all three graphs intersect. The graphs of all three equations intersect at exactly one point, (−1, 3). Therefore, the system of equations has one solution.
Choice A is incorrect. A system of equations has no solutions when there is no point at which all the graphs intersect. Because the graphs of all three equations intersect at the point (−1, 3), there is a solution. Choice C is incorrect. The graphs of all three equations intersect at only one point, (−1, 3). Since there is no other such point, there cannot be two solutions. Choice D is incorrect and may result from counting the number of points of intersection of the graphs of any two equations, including the point of intersection of all three equations.