Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l }
y = x - 1 \
y ^ { 2 } = - 4 x
\end{array}$$
(i) $( - 1 , - 2 )$; (ii) $( 1,0 )$
A) (i) Yes; (ii) Yes
B) (i) $\mathrm { No }$; (ii) Yes
C) (i) $\mathrm { No }$; (ii) $\mathrm { No }$
D) (i) Yes; (ii) No

Question

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
y = x - 1 \
y ^ { 2 } = - 4 x
\end{array}$$
(i) $( - 1 , - 2 )$; (ii) $( 1,0 )$
A) (i) Yes; (ii) Yes
B) (i) $\mathrm { No }$; (ii) Yes
C) (i) $\mathrm { No }$; (ii) $\mathrm { No }$
D) (i) Yes; (ii) No

Quizplus · Accepted Answer

For (i) $(-1, -2)$, substituting $x = -1$ into $y = x - 1$ gives $y = -2$, which matches. Substituting $x = -1$ into $y^2 = -4x$ gives $y^2 = 4$, and since $y = -2$, $y^2 = 4$ is true. Thus, (i) is a solution.For (ii) $(1, 0)$, substituting $x = 1$ into $y = x - 1$ gives $y = 0$, which matches. However, substituting $x = 1$ into $y^2 = -4x$ gives $y^2 = -4$, which is not possible since $y^2$ cannot be negative for real numbers. Thus, (ii) is not a solution.

Determine If Each Ordered Pair Is a Solution to the Given