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Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

-5.1x+3y=1.2
3.2x-8y=p

In the system of equations, p is a constant. Which of the following describes all values of p for which the system has exactly one solution?

A.p can be any number
B.p can be any number except 1.2
C.p can be any number except -1.2
D.p=1.2

答案和解析

答案：A

解析：

Option A is correct. After rewriting the equations in slope-intercept form (y=mx+b), the slopes of the two equations are different and the constant p is part of the y-intercept. Since the slopes are different regardless of the value of p, the lines represented by the equations must always intersect at exactly one point. So there is always one solution for any value of p.