Solve the system by the method of substitution. $$\left\{ \begin{array} { l }
y = 2 x ^ { 2 } \
y = 38 x - 180
\end{array} \right.$$
A) $( - 1,2 ) , ( 1,2 )$
B) $( 9,162 ) , ( 10,200 )$
C) $( - 9,162 ) , ( - 10,200 )$
D) $( 1,2 )$
E)no solution exists

Question

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } 
y = 2 x ^ { 2 } \
y = 38 x - 180
\end{array} \right.$$
A) $( - 1,2 ) , ( 1,2 )$
B) $( 9,162 ) , ( 10,200 )$
C) $( - 9,162 ) , ( - 10,200 )$
D) $( 1,2 )$
E)no solution exists

Quizplus · Accepted Answer

Since both equations equal y, you can set them equal to each other: $2x^2 = 38x - 180$. Solving this quadratic equation by rearranging it to $2x^2 - 38x + 180 = 0$ and then factoring or using the quadratic formula gives the solutions for x. The solutions for x are 9 and 10. Substituting these back into either original equation to solve for y gives the pairs (9,162) and (10,200).

Solve the System by the Method of Substitution {y=2x2y=38x−180\left\{ \begin{array} { l } y = 2 x ^ { 2 } \\y = 38 x - 180\end{array} \right.{y=2x2y=38x−180​

Solve the System by the Method of Substitution $\left\{ \begin{array} { l } y = 2 x ^ { 2 } \\y = 38 x - 180\end{array} \right.$