x+y = 18 5y = x What is the solution (x,y) to the given system of equations?
Correct answer: A (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice A is correct. The second equation in the given system defines the value + = of x as 5y. Substituting 5y for x into the first equation yields 5 y y18 or = = 6y 18. Dividing each side of this equation by 6 yields y 3. Substituting 3 for ( )= = ( ) y in the second equation yields 5 3 x or x 15. Therefore, the solution x, y ( ) to the given system of equations is 15, 3 . Choice B is incorrect. Substituting 16 for x and 2 for y in the second equation ( )= ( ) yields 5 2 16, which is not true. Therefore, 16, 2 is not a solution to the given system of equations. Choice C is incorrect. Substituting 17 for x and 1 for y ( )= ( ) in the second equation yields 51 17, which is not true. Therefore, 17, 1 is not a solution to the given system of equations. Choice D is incorrect. Substituting ( )= 18 for x and 0 for y in the second equation yields 5 0 18, which is not true. ( ) Therefore, 18, 0 is not a solution to the given system of equations.
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