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Question 23 of 30

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M:C:MC:19

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SAT

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table attributes columnalign right center left columnspacing 2px end attributes row cell x squared plus y squared end cell equals 153 row y equals cell minus 4 x end cell end table

If left parenthesis x comma space y right parenthesis is a solution to the system of equations above, what is the value of x squared ?

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-51

Correct Answer: 
No

3

Correct Answer: 
No

9

Correct Answer: 
Yes

144

Correct Answer: 
No

View Correct Answer

Choice C is correct. The second equation gives y in terms of x, so a student can use this to rewrite the first equation in terms of x. Substituting -4x for y in the equation x squared plus y squared equals 153 gives x squared plus left parenthesis minus 4 x right parenthesis squared equals 153. This can be simplified to x squared space plus space 16 x squared space equals space 153 comma or 17 x squared space equals space 153. Since the question asks for the value of x squared comma not x, dividing both sides of 17 x squared space equals space 153 by 17 gives the answer: x squared space equals space 153 over 17 space equals space 9.

Choice A is not the correct answer. This answer may result from neglecting to square the coefficient –4 in y space equals space minus 4 x comma which would give y squared space equals space minus 4 x squared. Then the first equation would become x squared space minus space 4 x squared space equals space minus 3 x squared space equals space 153 comma which would give –51 as the value of x squared.

Choice B is not the correct answer. This answer may result from finding the value for x, not the value of x squared.

Choice D is not the correct answer. This answer may result from finding the value of y squared comma not x squared.

Question Difficulty: 
medium
Objective: 

Students must manipulate one equation for use in another, in order to solve for a given value, making use of familiar algebraic arrangements where appropriate.