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Algebra / Systems of two linear equations in two variables Difficulty: Easy

The graph of a system of linear equations is shown. What is the solution $(x, y)$ to the system?

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Explanation

Choice B is correct. A solution to a system of equations must be the solution to each equation in the system. It follows that if $(x, y)$ is a solution to the system, the point $(x, y)$ lies on the graph in the xy-plane of each equation in the system. The point that lies on each graph of the system of linear equations shown is their intersection point $left parenthesis 2 comma 4 right parenthesis$ . Therefore, the solution to the system is $left parenthesis 2 comma 4 right parenthesis$ .

Choice A is incorrect. The point $left parenthesis 0 comma 5 right parenthesis$ lies on one, but not both, of the graphs of the linear equations shown.

Choice C is incorrect. The point $left parenthesis 5 comma 10 right parenthesis$ lies on one, but not both, of the graphs of the linear equations shown.

Choice D is incorrect. The point $left parenthesis 10 comma 0 right parenthesis$ lies on one, but not both, of the graphs of the linear equations shown.