Determine if (-1,-4) is a Solution x+y< =-3 , (-1,-4)
The given question is asking to check whether the coordinate point (-1, -4) is a solution to the inequality x + y ≤ -3. To do this, you would need to substitute the x-coordinate and the y-coordinate of the point into the inequality to see if the resultant expression is true. If the inequality holds true after the substitution, then the point (-1, -4) is indeed a solution; if not, then it is not a solution to the given inequality.
$x + y \leq - 3$,$\left(\right. - 1 , - 4 \left.\right)$
Answer
Solution:
Step 1:
Substitute $x = -1$ and $y = -4$ into the inequality $x + y \leq -3$ to verify if the pair satisfies the condition. Compute $-1 + (-4) \leq -3$.
Step 2:
Perform the addition of $-1$ and $-4$. The result is $-5 \leq -3$.
Step 3:
Evaluate the inequality. Since $-5$ is less than or equal to $-3$, the inequality holds true.
Step 4:
The inequality being true indicates that the pair $(-1, -4)$ is indeed a solution to the inequality $x + y \leq -3$.
Knowledge Notes:
To determine whether an ordered pair is a solution to an inequality, you must:
Substitution: Replace the variables in the inequality with the values from the ordered pair.
Perform Arithmetic: Carry out any necessary arithmetic operations to simplify the inequality.
Evaluate the Inequality: Check if the resulting statement is true or false.
Conclusion: If the inequality is true, the ordered pair is a solution. If it is false, the ordered pair is not a solution.
Inequalities are mathematical expressions involving the symbols $>$ (greater than), $<$ (less than), $\geq$ (greater than or equal to), and $\leq$ (less than or equal to). They indicate the relationship between two values.
When dealing with inequalities, it is important to remember that multiplying or dividing both sides by a negative number reverses the inequality sign. However, this is not relevant for this particular problem since we are only substituting and evaluating without altering the inequality itself.
