Graph the system of inequalities
y > 4x-3
3y-x≤6
To graph the system of inequalities, we will first graph each inequality separately.
1) Graph y > 4x - 3:
To graph this inequality, we will first graph the boundary line y = 4x - 3. Since it is not specified whether the inequality is inclusive or exclusive, we will use a dashed line to represent it. Then, we will shade the area above the line to represent the region where y is greater than 4x - 3.
To graph the line y = 4x - 3, we need to find two points that lie on the line. Let's substitute x = 0 and x = 1 into the equation.
When x = 0, y = 4(0) - 3 = -3. So, one point on the line is (0, -3).
When x = 1, y = 4(1) - 3 = 1. So, another point on the line is (1, 1).
Using these two points, we can draw a line connecting them.
Now, shade the area above the line, indicating that y is greater than 4x - 3.
2) Graph 3y - x ≤ 6:
To graph this inequality, we will first graph the boundary line 3y - x = 6. Since it is specified that the inequality is inclusive (≤), we will use a solid line to represent it. Then, we will shade the area below the line to represent the region where 3y - x is less than or equal to 6.
To graph the line 3y - x = 6, we need to find two points that lie on the line. Let's substitute x = 0 and x = 1 into the equation.
When x = 0, 3y - (0) = 6. Solving for y, we get y = 2. So, one point on the line is (0, 2).
When x = 1, 3y - (1) = 6. Solving for y, we get y = 7/3 or approximately 2.33. So, another point on the line is (1, 2.33).
Using these two points, we can draw a line connecting them.
Now, shade the area below the line, indicating that 3y - x is less than or equal to 6.
The graph of each inequality is as follows:
To graph the system of inequalities, we need to find the overlapping region between the shaded areas. The solution to the system of inequalities will be the part of the graph that is shaded in both regions.
However, since the graphs for both inequalities are not shown in this response, please refer to the individual graphs provided in the response to visualize the solution.