Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l }
3 x - y = - 17 \
y = x ^ { 2 } + 7
\end{array}$$
(i) $( 5,32 )$; (ii) $( - 2,11 )$
A) (i) Yes; (ii) No
B) (i) No; (ii) Yes
C) (i) No; (ii) No
D) (i) Yes; (ii) Yes

Question

Determine if each ordered pair is a solution to the given system of inequalities in two variables.
-$$\begin{array} { l } 
3 x - y = - 17 \
y = x ^ { 2 } + 7
\end{array}$$
(i) $( 5,32 )$; (ii) $( - 2,11 )$
A) (i) Yes; (ii) No
B) (i) No; (ii) Yes
C) (i) No; (ii) No
D) (i) Yes; (ii) Yes

Quizplus · Accepted Answer

For (i) $ (5,32) $, substituting $ x = 5 $ into the equations gives $ 3(5) - y = -17 $ and $ y = 5^2 + 7 $. The first equation simplifies to $ 15 - y = -17 $, which does not directly relate to the solution, but checking the second equation, $ y = 25 + 7 = 32 $, which matches, indicating the first equation was incorrectly assessed. Correctly, $ 3(5) - 32 = 15 - 32 = -17 $, so both conditions are satisfied. For (ii) $ (-2,11) $, substituting $ x = -2 $ gives $ 3(-2) - y = -17 $ and $ y = (-2)^2 + 7 $. The first equation simplifies to $ -6 - y = -17 $, and the second to $ y = 4 + 7 = 11 $. For the first equation, correctly solving for $ y $ gives $ -6 - y = -17 $ or $ y = 11 $, which matches the given $ y $ value. Thus, both ordered pairs satisfy the given system of inequalities.

Determine If Each Ordered Pair Is a Solution to the Given