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

$y = 3 x + 9$ $y = 3 x + 9$

$3 y = 8 x - 6$ $3 y = 8 x - 6$

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

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Explanation

Choice D is correct. The first equation in the given system of equations defines $y$ $y$ as $3 x + 9$ $3 x plus 9$ . Substituting $3 x + 9$ $3 x plus 9$ for $y$ $y$ in the second equation in the given system of equations yields $3 (3 x + 9) = 8 x - 6$ $3 (3 x + 9) = 8 x - 6$ . Applying the distributive property on the left-hand side of this equation yields $9 x + 27 = 8 x - 6$ $9 x + 27 = 8 x - 6$ . Subtracting $8 x$ $8 x$ from both sides of this equation yields $x + 27 = - 6$ $x + 27 = - 6$ . Subtracting $27$ $27$ from both sides of this equation yields $x = - 33$ $x = - 33$ . Substituting $- 33$ $negative 33$ for $x$ $x$ in the first equation of the given system of equations yields $y = 3 (- 33) + 9$ $y = 3 (- 33) + 9$ , or $y = - 90$ $y = - 90$ . Substituting $- 33$ $negative 33$ for $x$ $x$ and $- 90$ $negative 90$ for $y$ $y$ into the expression $x - y$ $x - y$ yields $- 33 - (- 90)$ $- 33 - (- 90)$ , or $57$ $57$ .

Choice A is incorrect. This is the value of $x + y$ $x + y$ , not $x - y$ $x - y$ .

Choice B is incorrect. This is the value of $x$ $x$ , not $x - y$ $x - y$ .

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