Solve the following system of linear inequalities by graphing.
3x+4y<=12
x+3y<=6
x>=0
y>=0
Try this site:
http://www.purplemath.com/modules/ineqgrph.htm
To solve the system of linear inequalities by graphing, we need to plot the individual graphs of each inequality and find the region where all the graphs overlap.
First, let's graph the inequality 3x + 4y ≤ 12. To do this, let's rewrite the inequality as an equation:
3x + 4y = 12.
Next, we need to find two points on this line. We can choose any values of x and solve for y, or vice versa. For simplicity, let's let x = 0 and solve for y:
3(0) + 4y = 12
4y = 12
y = 3.
So, one point on the line is (0, 3). Now, let's choose another value, say y = 0, and solve for x:
3x + 4(0) = 12
3x = 12
x = 4.
Another point on the line is (4, 0). Plot these two points on the graph and draw a straight line connecting them.
Next, let's graph the inequality x + 3y ≤ 6. Rewrite it as an equation:
x + 3y = 6.
For this equation, let's again choose x = 0 and solve for y:
0 + 3y = 6
3y = 6
y = 2.
The point (0, 2) is on the line. Now, let's choose y = 0 and solve for x:
x + 3(0) = 6
x = 6.
The point (6, 0) is also on the line. Plot these two points and draw a line connecting them.
Now, let's shade the region of the graph that satisfies the inequalities x ≥ 0 and y ≥ 0. These inequalities mean that x and y must be greater than or equal to zero, so the region that satisfies them is the first quadrant of the coordinate plane (the area above and to the right of the origin).
Now, observe the region where the two lines intersect and the shaded region of the first quadrant. The area where all the lines overlap and are shaded is the solution to the system of linear inequalities.
You can also use the provided website, http://www.purplemath.com/modules/ineqgrph.htm, as it allows you to input the inequalities and see the graphed solution.