Solve the system of equations algebraically for real values of x and y. $$\left\{ \begin{array} { l }
x ^ { 2 } - 8 x - y = - 15 \
x ^ { 2 } - 8 x + y = - 15
\end{array} \right.$$
A) $\quad ( 4,0 ) , ( 5,0 )$
B) $\quad ( 0,4 ) , ( 3,0 )$
C) $\quad ( 0,4 ) , ( 0,5 )$
D) $( 3,0 ) , ( 5,0 )$
E) no solution

Question

Solve the system of equations algebraically for real values of x and y. $$\left\{ \begin{array} { l } 
x ^ { 2 } - 8 x - y = - 15 \
x ^ { 2 } - 8 x + y = - 15
\end{array} \right.$$
A) $\quad ( 4,0 ) , ( 5,0 )$
B) $\quad ( 0,4 ) , ( 3,0 )$
C) $\quad ( 0,4 ) , ( 0,5 )$
D) $( 3,0 ) , ( 5,0 )$
E) no solution

Quizplus · Accepted Answer

The system of equations simplifies to $y = 0$. Substituting $y = 0$ into either equation gives $x^2 - 8x = -15$, which simplifies to $(x-3)(x-5) = 0$. Thus, the solutions are $x = 3$ and $x = 5$, with $y = 0$.

Solve the System of Equations Algebraically for Real Values of X