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Mathematics>Standard Multiple Choice

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

y=x^2+9
y=6x

If (x,y) is a solution to the system of equations shown above, which of the following is the y-coordinate of the solution?

(A) -18
(B) -3
(C) 3
(D) 18

答案和解析

答案：D

解析：

Choice D is correct.

Because both equations express y in terms of x, set the x-expressions equal to each other and solve. x^2+9= 6x
Determine the x-coordinates in the solution set by setting this quadratic equation equal to zero and factoring (alternatively, we could use the quadratic formula or complete the square).
x^2+9= 6x
x^2-6x+9=0
(x-3)(x-3)=0
Next, set each factor equal to zero and solve. Since the two factors are the same, this only needs to be done once.
x-3=0, x=3
x=3 is the x-coordinate of the solution set. In order to find the y-coordinate of the solution set, substitute this value of x into one of the original equations. In this case, it's easiest to substitute into the linear equation.
y=6x, y=6*3=18
The y-coordinate of the solution of the system of equations is 18.