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Nonlinear equations in one variable and systems of equations in two variables SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

$Equation 1: x plus y equals 17. Equation 2: x y equals 72.$

If one solution to the system of equations above is $the ordered pair x comma y$ , what is one possible value of x ?

Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.

ExplanationShow

The correct answer is either 8 or 9. The first equation can be rewritten as $y equals, 17 minus x$ . Substituting $17 minus x$ for y in the second equation gives $x times, open parenthesis, 17 minus x, close parenthesis, equals 72$ . By applying the distributive property, this can be rewritten as $17 x, minus x squared, equals 72$ . Subtracting 72 from both sides of the equation yields $x squared, minus 17 x, plus 72, equals 0$ . Factoring the left-hand side of this equation yields $open parenthesis, x minus 8, close parenthesis, times, open parenthesis, x minus 9, close parenthesis, equals 0$ . Applying the Zero Product Property, it follows that $x minus 8, equals 0$ and $x minus 9, equals 0$ . Solving each equation for x yields $x equals 8$ and $x equals 9$ respectively. Note that 8 and 9 are examples of ways to enter a correct answer.

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Nonlinear equations in one variable and systems of equations in two variables SAT question

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