Hi,
What point is a solution to the system of inequalities y >4x and y >-2x-3
(1/2,2)?
well, does (1/2,2) fit both conditions?
No. 2 is not greater than (4)(1/2).
rearranging things a bit,
4x - y > 0
2x + y > -3
Adding the two equations,
6x > -3
x > -1/2
-2x-3 < y < 4x
To determine if the point (1/2, 2) is a solution to the system of inequalities y > 4x and y > -2x - 3, follow these steps:
Step 1: Substitute the x and y values of the point into the first inequality: y > 4x
2 > 4(1/2)
Step 2: Simplify the inequality:
2 > 2
Step 3: Determine if the inequality is true. In this case, it is not true because 2 is not greater than 2.
Therefore, (1/2, 2) is not a solution to the inequality y > 4x.
Now, let's check if the point (1/2, 2) is a solution to the second inequality: y > -2x - 3.
Step 1: Substitute the x and y values of the point into the second inequality: y > -2x - 3
2 > -2(1/2) - 3
Step 2: Simplify the inequality:
2 > -1 - 3
2 > -4
Step 3: Determine if the inequality is true. In this case, it is true because 2 is greater than -4.
Therefore, (1/2, 2) is a solution to the inequality y > -2x - 3.
To summarize, the point (1/2, 2) is a solution to the inequality y > -2x - 3, but not a solution to the inequality y > 4x.
To determine if the point (1/2, 2) is a solution to the system of inequalities y > 4x and y > -2x - 3, you need to substitute the values of x and y into the inequalities and check if both inequalities are satisfied.
Let's start by substituting x = 1/2 and y = 2 into the first inequality: y > 4x.
2 > 4(1/2)
2 > 2
The inequality 2 > 2 is not true. Therefore, (1/2, 2) does not satisfy the first inequality y > 4x.
Now, let's check the second inequality y > -2x - 3 with the same values of x and y:
2 > -2(1/2) - 3
2 > -1 - 3
2 > -4
The inequality 2 > -4 is true. Hence, (1/2, 2) satisfies the second inequality y > -2x - 3.
In conclusion, the point (1/2, 2) is a solution to the system of inequalities y > 4x and y > -2x - 3 because it satisfies the second inequality, but it does not satisfy the first inequality.