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

$y - 9 x = 13$

$5 x equals 2 y$

What is the solution $(x, y)$ to the given system of equations?

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Explanation

Choice C is correct. Adding $9 x$ to both sides of the first equation in the given system yields $y = 9 x + 13$ . Substituting the expression $9 x plus 13$ for $y$ in the second equation in the given system yields $5 x = 2 (9 x + 13)$ . Distributing the $2$ on the right-hand side of this equation yields $5 x = 18 x + 26$ . Subtracting $18 x$ from both sides of this equation yields $- 13 x = 26$ . Dividing both sides of this equation by $negative 13$ yields $x = - 2$ . Substituting $negative 2$ for $x$ in the equation $y = 9 x + 13$ yields $y = 9 (- 2) + 13$ , or $y = - 5$ . Therefore, the solution $(x, y)$ to the given system of equations is $(- 2, - 5)$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the solution $(y, x)$ , not $(x, y)$ , to the given system of equations.