Asked by Dusty Dawson on May 21, 2024
Verified
Determine if the ordered pair (18,0) ( 18,0 ) (18,0) is a solution of the system of linear inequalities {3x−y>4x+6y≤9\left\{ \begin{array} { l } 3 x - y > 4 \\x + 6 y \leq 9\end{array} \right.{3x−y>4x+6y≤9 .
A) not a solution
B) solution
Linear Inequalities
Mathematical expressions that represent a range of values along a line where one side of the inequality has a variable term.
Solution
The numbers that fulfill the requirements of an equation, inequality, or a set of equations.
- Depict graphically the systems of linear inequalities in a two-dimensional space.
Verified Answer
IS
Inayat SinghMay 23, 2024
Final Answer :
A
Explanation :
For the first inequality, plugging in the values $(18,0)$, we get:
$3(18)-0>4$ which simplifies to $54>4$
This is true!
For the second inequality, plugging in the values $(18,0)$, we get:
$18+6(0) \leq 9$ which simplifies to $18 \leq 9$
This is false!
So the ordered pair $(18,0)$ does not satisfy the system of linear inequalities and is not a solution. Therefore, the answer is choice A.
$3(18)-0>4$ which simplifies to $54>4$
This is true!
For the second inequality, plugging in the values $(18,0)$, we get:
$18+6(0) \leq 9$ which simplifies to $18 \leq 9$
This is false!
So the ordered pair $(18,0)$ does not satisfy the system of linear inequalities and is not a solution. Therefore, the answer is choice A.
Learning Objectives
- Depict graphically the systems of linear inequalities in a two-dimensional space.
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