What point is a solution to the system of inequalities y(inequality arrow pointing right)4x and y(inequality arrow pointing right)-2x-3?
-1/2,-2?
y > 4x AND y > -2x - 3
sketch y = 4x and draw the line as a dotted line
sketch y = -2x - 3 and draw the line as a dotted line
shade in the region which lies above BOTH lines
Any point in that region will do.
There is an infinite number of such points.
e.g. (-1,5) is one of them
Thank you!
To find the solution to the system of inequalities y > 4x and y > -2x - 3, we need to find the values of x and y that satisfy both inequalities.
For the first inequality, y > 4x, we can plot the line y = 4x and shade the region above the line to represent the inequality.
The second inequality, y > -2x - 3, can be plotted as the line y = -2x - 3 and shade the region above this line as well.
Now, to find the overlapped region that satisfies both inequalities, we need to consider the shaded region above both lines.
The point (-1/2, -2) falls within this overlapped region and satisfies both inequalities. Therefore, (-1/2, -2) is a possible solution to the system of inequalities y > 4x and y > -2x - 3.
To determine if the point (-1/2, -2) is a solution to the system of inequalities y > 4x and y > -2x - 3, we need to check if it satisfies both inequalities.
1. y > 4x:
Substituting the x and y values of (-1/2, -2) into the first inequality:
-2 > 4(-1/2)
-2 > -2
Since this inequality is false, (-1/2, -2) does not satisfy y > 4x.
2. y > -2x - 3:
Substituting the x and y values of (-1/2, -2) into the second inequality:
-2 > -2(-1/2) - 3
-2 > 1 - 3
-2 > -2
This inequality is true since -2 is greater than -2.
Since (-1/2, -2) satisfies the second inequality y > -2x - 3, it is a solution to the system of inequalities.
In summary, the given point (-1/2, -2) is a solution to the system of inequalities y > 4x and y > -2x - 3.