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Systems of two linear equations in two variables SAT question

Math · Algebra · Easy · Answer it here, explanation included.

$Equation 1: x plus y, equals 20. Equation 2: 2 times, open parenthesis, x plus y, close parenthesis, plus 3 y, equals 85.$

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

ExplanationShow

Choice B is correct. Substituting 20 for $x plus y$ in the second equation in the system yields $2 times 20, plus 3y, equals 85$ , or $40 plus 3 y, equals 85$ . Subtracting 40 from both sides of this equation yields $3 y equals 45$ . Dividing both sides of this equation by 3 yields $y equals 15$ .

Choice A is incorrect. If $y equals 10$ , then $x equals 10$ since $x plus y, equals 20$ . However, substituting 10 for both x and y in the second equation yields $70 equals 85$ , which is a false statement. Choice C is incorrect. If $y equals 60$ , then $x equals negative 40$ since $x plus y, equals 20$ . However, substituting these values for x and y in the second equation yields $220 equals 85$ , which is a false statement. Choice D is incorrect. If $y equals 65$ , then $x equals negative 45$ since $x plus y, equals 20$ . However, substituting these values for x and y in the second equation yields $235 equals 85$ , which is a false statement.

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Systems of two linear equations in two variables SAT question

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