Which is a solution of the systems of linear inequality in two variables x + y > 7 and y - x < 3?
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Answer:
C. (6, 3)
Step-by-step explanation:
To determine whether an ordered pair is a solution to the system of linear inequalities, substitute its coordinates to the inequalities for each variable and check if the inequality is true. If the resulting inequality is true, then the ordered pair is a solution; if not, then the ordered pair is not a solution.
We are given the system of linear inequalities:
[tex]\begin{cases} x+y>7 \\ y-x < 3\end{cases}[/tex]
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Checking A. (2, -4):
[tex]\begin{cases} 2+(-4)>7 \implies -2>7 \quad \textsf{(false)} \\ -4 - 2<3 \implies -6 <3 \end{cases}[/tex]
(not solution)
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Checking B. (-2, -5):
[tex]\begin{cases} -2 + (-5) > 7 \implies -7 > 7 \quad \textsf{(false}) \\ -5 - (-2) < 3 \implies -3 < 3\end{cases}[/tex]
(not solution)
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Checking C. (6, 3):
[tex]\begin{cases} 6+3 > 7 \implies 9 > 7 \\ 3-6 < 3 \implies -3 < 3\end{cases}; \quad \textsf{(both true)}[/tex]
(solution)
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Therefore, the correct answer is C. (6, 3)
