Solve by graphing. Check your solution.
y > 2
y > -x + 2
Am I supposed to graph this one on a line or on an actual graph? Thank you.
An actual graph. Plot the two "equal" lines and shade the regions above each ine. The answer is the region above BOTH lines. It will be wedge shaped, with the point where the lines intersect
To graph the system of inequalities y > 2 and y > -x + 2, you would plot them on an actual graph. Here are the steps to do this:
1. Draw a coordinate plane with x and y axes.
2. Start by graphing the first inequality, y > 2. Draw a horizontal dotted line across the graph at y = 2. Since the inequality is y > 2, the area above the line should be shaded.
3. Now graph the second inequality, y > -x + 2. To do this, rewrite it in slope-intercept form, y = -x + 2. The line has a y-intercept of 2 and a slope of -1. Draw the line passing through (0, 2), and since the inequality is y > -x + 2, the area above the line should be shaded as well.
By shading the areas above each line, you will have shaded regions that overlap. The region where both inequalities are true represents the solution to the system of inequalities.
To check the solution, choose a point within the shaded region and substitute its x and y coordinates into the original inequalities. If both inequalities are true, the solution is correct.