Solve the system of two linear inequalities graphically. y-7x>7 y>-2 Find the region with points that satisfy both inequalities. Select the region you wish to be shaded: A, B, C or D
To graphically solve the system of two linear inequalities, we start by graphing each individual inequality and then identify the region that satisfies both inequalities.
1. Graph the first inequality, y - 7x > 7:
To graph this inequality, we can start by graphing the equation y - 7x = 7.
Rearranging this equation, we get y = 7x + 7 which is in the slope-intercept form (y = mx + b).
Let's find two points on this line:
When x = 0, y = 7(0) + 7 = 7. So, we have the point (0, 7).
When x = 1, y = 7(1) + 7 = 14. So, we have the point (1, 14).
Plot these two points and draw a line passing through them. Note that the line should be dashed since the inequality is greater than (>) (not greater than or equal to).
2. Graph the second inequality, y > -2:
To graph this inequality, we need to draw a horizontal line at y = -2. Note that the line should be solid (since the inequality includes equal to (=)) and does not pass through (0, -2).
3. Find the region that satisfies both inequalities:
Now, we need to find the region that satisfies both inequalities. This is done by comparing the graphs of the two inequalities.
Region A will be shaded since it represents the region where both inequalities are satisfied.