Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l r }
x - y & = 3 \
x ^ { 2 } - y ^ { 2 } & = 45
\end{array} \right)$$
A) ( $-$ 9, 6)
B) (6, 9)
C) (9, $-$ 6)
D) (9, 6)

Question

Solve the system by the substitution or elimination method. $$\left( \begin{array} { r l r } 
x - y & = 3 \
x ^ { 2 } - y ^ { 2 } & = 45
\end{array} \right)$$
A) ( $-$ 9, 6)
B) (6, 9)
C) (9, $-$ 6)
D) (9, 6)

Quizplus · Accepted Answer

From the first equation, we have $x = y + 3$. Substituting this into the second equation, we get:$$(y + 3)^2 - y^2 = 45$$$$y^2 + 6y + 9 - y^2 = 45$$$$6y = 36$$$$y = 6$$Substituting this back into the first equation, we get:$$x - 6 = 3$$$$x = 9$$Therefore, the solution is (9, 6).

Solve the System by the Substitution or Elimination Method (x−y=3x2−y2=45)\left( \begin{array} { r l r } x - y & = 3 \\x ^ { 2 } - y ^ { 2 } & = 45\end{array} \right)(x−yx2−y2​=3=45​)

Solve the System by the Substitution or Elimination Method $\left( \begin{array} { r l r } x - y & = 3 \\x ^ { 2 } - y ^ { 2 } & = 45\end{array} \right)$