Solve Nonlinear Systems By Substitution
-$$\begin{array} { l }
2 y - x = 10 \
x ^ { 2 } + y ^ { 2 } - 100 = 0
\end{array}$$
A) $\{ ( - 10,0 ) , ( 6,8 ) \}$
B) $\{ ( 10,0 ) , ( - 10,0 ) , ( 6,8 ) \}$
C) $\{ ( 0,5 ) , ( 8,9 ) \}$
D) $\{ ( 0,5 ) , ( 0 , - 5 ) , ( 8,9 ) \}$

Question

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
2 y - x = 10 \
x ^ { 2 } + y ^ { 2 } - 100 = 0
\end{array}$$
A) $\{ ( - 10,0 ) , ( 6,8 ) \}$
B) $\{ ( 10,0 ) , ( - 10,0 ) , ( 6,8 ) \}$
C) $\{ ( 0,5 ) , ( 8,9 ) \}$
D) $\{ ( 0,5 ) , ( 0 , - 5 ) , ( 8,9 ) \}$

Quizplus · Accepted Answer

From the first equation, solve for $x$ to get $x = 2y - 10$. Substitute $x$ in the second equation to get $(2y - 10)^2 + y^2 - 100 = 0$. Solve this equation for $y$ to find the corresponding $x$ values. The solutions are $(-10, 0)$ and $(6, 8)$.

Solve Nonlinear Systems by Substitution - 2y−x=10x2+y2−100=0\begin{array} { l } 2 y - x = 10 \\x ^ { 2 } + y ^ { 2 } - 100 = 0\end{array}2y−x=10x2+y2−100=0​

Solve Nonlinear Systems by Substitution
- $\begin{array} { l } 2 y - x = 10 \\x ^ { 2 } + y ^ { 2 } - 100 = 0\end{array}$