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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.

$y equals, x squared, minus 4 x, plus 4, and y equals, 4 minus x$

If the ordered pair $x comma y$ satisfies the system of equations above, 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 0 or 3. For an ordered pair to satisfy a system of equations, both the x- and y-values of the ordered pair must satisfy each equation in the system. Both expressions on the right-hand side of the given equations are equal to y, therefore it follows that both expressions on the right-hand side of the equations are equal to each other: $x squared, minus 4 x, plus 4, equals, 4 minus x$ . This equation can be rewritten as $x squared, minus 3 x, equals 0$ , and then through factoring, the equation becomes $x times, open parenthesis, x minus 3, close parenthesis, equals 0$ . Because the product of the two factors is equal to 0, it can be concluded that either $x equals 0$ or $x minus 3, equals 0$ , or rather, $x equals 0$ or $x equals 3$ . Note that 0 and 3 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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