Solve the system by the substitution method.
-$$\begin{array} { l }
y = x ^ { 2 } + 1 \
- 4 x - y = 2
\end{array}$$
A) $\{ ( - 1,2 ) , ( - 3,10 ) \}$
B) \{ \}
C) $\{ ( 1,2 ) , ( - 1,2 ) \}$
D) $( 0,1 ) , ( 0 , - 2 ) \}$

Question

Solve the system by the substitution method.
-$$\begin{array} { l } 
y = x ^ { 2 } + 1 \
- 4 x - y = 2
\end{array}$$
A) $\{ ( - 1,2 ) , ( - 3,10 ) \}$
B) \{ \}
C) $\{ ( 1,2 ) , ( - 1,2 ) \}$
D) $( 0,1 ) , ( 0 , - 2 ) \}$

Quizplus · Accepted Answer

Substitute $y = x^2 + 1$ into the second equation to get $-4x - (x^2 + 1) = 2$, which simplifies to $x^2 + 4x + 3 = 0$. Factoring gives $(x + 1)(x + 3) = 0$, so $x = -1$ or $x = -3$. Substituting these values back into $y = x^2 + 1$ gives the pairs $(-1, 2)$ and $(-3, 10)$.

Solve the System by the Substitution Method y=x2+1−4x−y=2\begin{array} { l } y = x ^ { 2 } + 1 \\- 4 x - y = 2\end{array}y=x2+1−4x−y=2​

Solve the System by the Substitution Method $\begin{array} { l } y = x ^ { 2 } + 1 \\- 4 x - y = 2\end{array}$