|
Question 1090670: Determine whether or not the given point is a solution to the given
system of inequalities.
(−3/2, 1/3)
x − 2y ≤ 4
y ≤ |3x − 1| + 2
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
If you want to just blindly perform mathematical operations to answer this question, you can simply plug the x and y values of the given point into the two inequalities and see if both inequalities are satisfied. The work might look something like this....
Yes, -13/6 is less than 4; the first inequality is satisfied.
y = 1/3 is less than 15/2, so the second inequality is also satisfied.
But you don't need to go to all that work. You can use logical reasoning without any need to do any detailed calculations to see that both inequalities are satisfied.
In the first inequality, you are starting with a negative value (x is negative), and you are subtracting a positive value (y is positive), so the result is clearly a negative number. But you don't care what negative number it is, because ANY negative number is less than 4.
For the second inequality, the value of the absolute value part of the expression on the right is 0 or positive; so when you add 2, the value of the entire expression on the right is 2 or greater. And again you don't care what the exact value of the expression is for the given x value, because ANY number that is greater than or equal to 2 is greater than the given y value 1/3.
|
|
|
| |
