Solve the system $\left\{ \begin{array} { r }
x ^ { 2 } + y ^ { 2 } = 49 \
x - y = 3
\end{array} \right.$ by substitution. Which of the following equations is the outcome, when substituting the equation $x - y = 3$ into $x ^ { 2 } + y ^ { 2 } = 49$ ?
A) $2 y ^ { 2 } + 9 = 49$
B) $2 y ^ { 2 } + 6 y + 9 = 49$
C) $2 y ^ { 2 } + y + 9 = 49$
D) $2 y ^ { 4 } + 9 = 49$

Question

Solve the system $\left\{ \begin{array} { r } 
x ^ { 2 } + y ^ { 2 } = 49 \
x - y = 3
\end{array} \right.$ by substitution. Which of the following equations is the outcome, when substituting the equation $x - y = 3$ into $x ^ { 2 } + y ^ { 2 } = 49$ ?
A) $2 y ^ { 2 } + 9 = 49$
B) $2 y ^ { 2 } + 6 y + 9 = 49$
C) $2 y ^ { 2 } + y + 9 = 49$
D) $2 y ^ { 4 } + 9 = 49$

Quizplus · Accepted Answer

From the equation $x - y = 3$, we can express $x$ as $x = y + 3$. Substituting $x = y + 3$ into $x^2 + y^2 = 49$, we get $(y + 3)^2 + y^2 = 49$. Expanding $(y + 3)^2$ gives $y^2 + 6y + 9 + y^2 = 49$, which simplifies to $2y^2 + 6y + 9 = 49$.

Solve the System {x2+y2=49x−y=3\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 49 \\x - y = 3\end{array} \right.{x2+y2=49x−y=3​

Solve the System $\left\{ \begin{array} { r } x ^ { 2 } + y ^ { 2 } = 49 \\x - y = 3\end{array} \right.$