Solve Nonlinear Systems By Substitution
-$$\begin{array} { l }
x + y = 5 \
y = x ^ { 2 } - 6 x + 9
\end{array}$$
A) $\{ ( 4,1 ) , ( 1,4 ) \}$
B) $\{ ( - 4,9 ) , ( - 1,6 ) \}$
C) $\{ ( 3,2 ) \}$
D) $\{ ( 4,9 ) , ( 1,4 ) \}$

Question

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
x + y = 5 \
y = x ^ { 2 } - 6 x + 9
\end{array}$$
A) $\{ ( 4,1 ) , ( 1,4 ) \}$
B) $\{ ( - 4,9 ) , ( - 1,6 ) \}$
C) $\{ ( 3,2 ) \}$
D) $\{ ( 4,9 ) , ( 1,4 ) \}$

Quizplus · Accepted Answer

Substitute $y = x^2 - 6x + 9$ into $x + y = 5$, giving $x + x^2 - 6x + 9 = 5$. Simplifying, $x^2 - 5x + 4 = 0$, which factors to $(x-4)(x-1) = 0$. Thus, $x = 4$ or $x = 1$. Substituting these values back into either original equation gives the pairs $(4, 1)$ and $(1, 4)$.

Solve Nonlinear Systems by Substitution - x+y=5y=x2−6x+9\begin{array} { l } x + y = 5 \\y = x ^ { 2 } - 6 x + 9\end{array}x+y=5y=x2−6x+9​

Solve Nonlinear Systems by Substitution
- $\begin{array} { l } x + y = 5 \\y = x ^ { 2 } - 6 x + 9\end{array}$