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

$y = 6 x + 16$

$- 7 x - y = 36$

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

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Explanation

Choice A is correct. The given system of linear equations can be solved by the substitution method. The first equation in the given system of equations defines $y$ as $6 x plus 16$ . Substituting $6 x plus 16$ for $y$ in the second equation of the given system of equations yields $- 7 x - (6 x + 16) = 36$ . Applying the distributive property on the left-hand side of this equation yields $- 7 x - 6 x - 16 = 36$ , or $- 13 x - 16 = 36$ . Adding $16$ to both sides of this equation yields $- 13 x = 52$ . Dividing both sides of this equation by $negative 13$ yields $x = - 4$ . Substituting $negative 4$ for $x$ in the first equation of the given system of equations, $y = 6 x + 16$ , yields $y = 6 (- 4) + 16$ , or $y = - 8$ . Therefore, the solution $(x, y)$ to the given system of equations is $(- 4, - 8)$ .

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

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

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