The first three steps in determining the solution set of the system of equations, y is equal to negative x squared minus 2 x plus 8 and y is equal to 2 x plus 11 , algebraically are shown in the table. Step Equation Step 1 negative x squared minus 2 x plus 8 is equal to 2 x plus 11 Step 2 0 is equal to x squared plus 4 x plus 3 Step 3 0 is equal to open paren x plus 1 close paren times open paren x plus 3 close paren Which represents the solution(s) of this system of equations?
Answer
A
negative 3 comma negative 1
B
negative 3 comma 5 and negative 1 comma 9
C
negative 3 comma 5
D
1 comma 13 and 3 comma 20
Explanation
The factored equation is (x + 1)(x + 3) = 0, so the x-values are −1 and −3. Substitute each into y = 2x + 11: when x = −1, y = 9; when x = −3, y = 5. The solutions are (−3, 5) and (−1, 9), which is choice B.
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