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

The sum of a number $x$ $x$ and $7$ is twice as large as a number $y$ . The number $y$ is $3$ less than the number $x$ . Which system of equations describes this situation?

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Explanation

Choice A is correct. It's given that the sum of a number $x$ and $7$ is twice as large as a number $y$ . This can be described by the equation $x + 7 = 2 y$ . It’s also given that the number $y$ is $3$ less than the number $x$ . This can be described by the equation $y = x - 3$ . Therefore, the system consisting of the equations $x + 7 = 2 y$ and $y = x - 3$ describes this situation.

Choice B is incorrect. The equation $y = 3 - x$ describes a situation where the number $y$ is $x$ less than $3$ .

Choice C is incorrect. The equation $2 (x + 7) = y$ describes a situation where the number $y$ is twice the sum of a number $x$ and $7$ .

Choice D is incorrect. The equation $2 (x + 7) = y$ describes a situation where the number $y$ is twice the sum of a number $x$ and $7$ , and the equation $y = 3 - x$ describes a situation where a number $y$ is $x$ less than $3$ .