the points of intersection of the graphs of the equations:
$\begin{array} { l }
x = y ^ { 2 } - 3 \
y = x + 1
\end{array}$
A) $( - 2,1 ) , ( - 1,2 )$
B) $( - 2,0 ) , ( 1,2 )$
C) $( - 2 , - 1 ) , ( 1,2 )$
D) $( 2 , - 1 ) , ( - 1,2 )$
E) $( - 2 , - 3 ) , ( - 1,2 )$

Question

the points of intersection of the graphs of the equations: 
$\begin{array} { l } 
x = y ^ { 2 } - 3 \
y = x + 1
\end{array}$
A) $( - 2,1 ) , ( - 1,2 )$
B) $( - 2,0 ) , ( 1,2 )$
C) $( - 2 , - 1 ) , ( 1,2 )$
D) $( 2 , - 1 ) , ( - 1,2 )$
E) $( - 2 , - 3 ) , ( - 1,2 )$

Quizplus · Accepted Answer

Substitute $y = x + 1$ into $x = y^2 - 3$, resulting in $x = (x + 1)^2 - 3$. Solving this equation gives $x = -2$ and $x = 1$. Substituting these values back into $y = x + 1$ gives the points $(-2, -1)$ and $(1, 2)$.

The Points of Intersection of the Graphs of the Equations x=y2−3y=x+1\begin{array} { l } x = y ^ { 2 } - 3 \\y = x + 1\end{array}x=y2−3y=x+1​

The Points of Intersection of the Graphs of the Equations $\begin{array} { l } x = y ^ { 2 } - 3 \\y = x + 1\end{array}$