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${:[y=-x-11],[y=x^(2)-5x-7]:} Which of the following is a solution to the system of equations? Choose 1 answer: (A) (-2,-9) (B) (0,-7) (C) (2,-13) (D) (3,-13)$

$y=-x-11$ $\newline$ $y=x^2-5x-7$ $\newline$ Which of the following is a solution to the system of equations? $\newline$ Choose $1$ answer: $\newline$ (A) $(-2,-9)$ $\newline$ (B) $(0,-7)$ $\newline$ (C) $(2,-13)$ $\newline$ (D) $(3,-13)$

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Math Problems

Algebra 2

Simplify rational expressions

Full solution

y=-x-11

\newline

y=x^2-5x-7

\newline

Which of the following is a solution to the system of equations?

\newline

Choose

1

answer:

\newline

(A)

(-2,-9)

\newline

(B)

(0,-7)

\newline

(C)

(2,-13)

\newline

(D)

(3,-13)

Plug $x$ -values in second equation: First, let's plug in the $x$ -values from each option into the second equation $y = x^2 - 5x - 7$ and see if they match the $y$ -values given.
Option (A): Option (A): For $x = -2$ , $y = (-2)^2 - 5(-2) - 7 = 4 + 10 - 7 = 7$ , but the option says $y = -9$ , so this ain't right.
Option (B): Option (B): For $x = 0$ , $y = 0^2 - 5(0) - 7 = -7$ , which matches the $y$ -value given in the option, but we gotta check the first equation too.
Option (C): Plug $x = 0$ into the first equation $y = -x - 11$ , we get $y = -0 - 11 = -11$ , which doesn't match the $y$ -value from option (B), so this ain't it either.
Option (D): Option (C): For $x = 2$ , $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ , which matches the y-value given in the option, let's check the first equation.
Option (D): Option (C): For $x = 2$ , $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ , which matches the $y$ -value given in the option, let's check the first equation.Plug $x = 2$ into the first equation $y = -x - 11$ , we get $y = -2 - 11 = -13$ , which matches the $y$ -value from option (C), so this looks good, but let's check the last option to be sure.
Option (D): Option (C): For $x = 2$ , $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ , which matches the $y$ -value given in the option, let's check the first equation.Plug $x = 2$ into the first equation $y = -x - 11$ , we get $y = -2 - 11 = -13$ , which matches the $y$ -value from option (C), so this looks good, but let's check the last option to be sure.Option (D): For $x = 3$ , $y = 3^2 - 5(3) - 7 = 9 - 15 - 7 = -13$ , which matches the $y$ -value given in the option, but we gotta check the first equation too.
Option (D): Option (C): For $x = 2$ , $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ , which matches the $y$ -value given in the option, let's check the first equation.Plug $x = 2$ into the first equation $y = -x - 11$ , we get $y = -2 - 11 = -13$ , which matches the $y$ -value from option (C), so this looks good, but let's check the last option to be sure.Option (D): For $x = 3$ , $y = 3^2 - 5(3) - 7 = 9 - 15 - 7 = -13$ , which matches the $y$ -value given in the option, but we gotta check the first equation too.Plug $x = 3$ into the first equation $y = -x - 11$ , we get $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ $2$ , but the option says $y = 2^2 - 5(2) - 7 = 4 - 10 - 7 = -13$ $3$ , so there's a mistake here, and option (D) is wrong.