y = x + 9\ny = x^{2}+16x + 63\na solution to the given system of equations is (x,y). what is the greatest…
y = x + 9\ny = x^{2}+16x + 63\na solution to the given system of equations is (x,y). what is the greatest possible value of x?\na -6\nb 7\nc 9\nd 63
Answer
Explanation:
Step1: Set the two equations equal
Since (y=x + 9) and (y=x^{2}+16x + 63), we set (x + 9=x^{2}+16x+63).
Step2: Rearrange to quadratic form
Move all terms to one - side: (x^{2}+16x + 63-(x + 9)=0), which simplifies to (x^{2}+16x+63 - x - 9 = 0), then (x^{2}+15x + 54=0).
Step3: Factor the quadratic equation
We factor (x^{2}+15x + 54) as ((x + 6)(x+9)=0).
Step4: Solve for x
Using the zero - product property, if ((x + 6)(x + 9)=0), then (x+6 = 0) or (x + 9=0). So (x=-6) or (x=-9).
Answer:
A. (-6)