Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order. Check the original PDF →
2x+3y = 7 10x+15y = 35 For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system? r
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The two given equations are equivalent because the second equation can be obtained from the first equation by multiplying each side of the equation by 5. Thus, the graphs of the equations are coincident, so if a point lies on the graph of one of the equations, it also lies on the graph of the other equation. A point ^x,yh lies on the graph of an equation in the xy-plane if and only 47 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 if this point represents a solution to the equation. It is sufficient, therefore, to find the point that represents a solution to the first given equation. Substituting the 3 7 x- and y-coordinates of choice B, - 2r+ 2 and r, for x and y, respectively, in the first equation yields 2 b - 3 2r+ 2 7 l +3 r =7 , which is equivalent to -3 r +7+3 r =7 , or 7 = 7. Therefore, the point ` - 3 2r+ 2 7, rj represents a solution to the first equation and thus lies on the graph of each equation in the xy-plane for the given system. Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
Loading…
Searched on YouTube by topic, not by question text. Open this search on YouTube →
Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.