graph solution set of system of inequalities
x+y< 4
x-2y>6
for y+y < 4
y < -x + 4
---> sketch y = -x+4, draw a dotted line for the equation and shade in the region below the line
for x-2y > 6
-y > -x + 6
y < x - 6
---> sketch y = x-6, draw a dotted line for the equation and shade in the region above the line
To graph the solution set of the system of inequalities, we need to plot the graph of each individual inequality and then shade the region that satisfies both inequalities.
Let's start with the first inequality: x + y < 4.
To graph this inequality, we can start by considering the equality: x + y = 4. This equation represents a straight line on the x-y plane. To plot this line, we need to find two points on it.
Let's choose x = 0. If x = 0, then y = 4, so one point is (0, 4).
Now let's choose y = 0. If y = 0, then x = 4, so another point is (4, 0).
Plot these two points on the graph and draw a straight line passing through them.
Next, we need to determine which side of the line to shade. Note that the inequality is "less than," so we need to shade the region below the line. This represents all points that satisfy the inequality x + y < 4.
Now let's move on to the second inequality: x - 2y > 6.
We can start by considering the equality: x - 2y = 6. This equation represents another straight line on the x-y plane. To plot this line, we need to find two points on it.
Again, let's choose x = 0. If x = 0, then -2y = 6, which implies y = -3. So one point is (0, -3).
Now let's choose y = 0. If y = 0, then x = 6, so another point is (6, 0).
Plot these two points on the graph and draw a straight line passing through them.
Finally, we need to determine which side of the line to shade. Note that the inequality is "greater than," so we need to shade the region above the line. This represents all points that satisfy the inequality x - 2y > 6.
Now, look at the two shaded regions on the graph. The solution set of the system of inequalities is the region where both shaded areas overlap. That is the region that satisfies both x + y < 4 and x - 2y > 6.