Solve the given system of linear inequalities by graphing:
x+y>4
x-y<7
x+y>4 will turn into y>-x+4 you will graph it like it says = instead of > and shade above the line.
x-y<7 will turn into y>x-7. Graph like there is an = and shade above the line with a different color.
Where the colors overlap will be the answer>
Using the following system of inequalities find the maximum value of f(x,y)=3x+2y
X>0
y>0
3x+2y<18
6x+7y<42
To solve the system of linear inequalities, you can use the method of graphing. Here is how you can do it:
Step 1: Graph the first inequality: x + y > 4
To graph this inequality, start by drawing a dashed line for the equation x + y = 4. Since this is a strict inequality (>), we use a dashed line instead of a solid line.
To draw the dashed line, find the intercepts by setting x and y to zero:
For x = 0, y = 4.
For y = 0, x = 4.
Now, plot these two points (0,4) and (4,0) on a graph and draw a dashed line passing through them.
Step 2: Shade the appropriate region:
Since the inequality is greater than (>), the shaded region will be above the line. Shade the region above the dashed line.
Step 3: Graph the second inequality: x - y < 7
To graph this inequality, start by drawing a dashed line for the equation x - y = 7. Again, since this is a strict inequality (<), we use a dashed line.
Find the intercepts by setting x and y to zero:
For x = 0, y = -7.
For y = 0, x = 7.
Now, plot these two points (0,-7) and (7,0) on the graph and draw a dashed line passing through them.
Step 4: Shade the appropriate region:
Since the inequality is less than (<), the shaded region will be below the line. Shade the region below the dashed line.
Step 5: Find the overlapping shaded region:
Finally, identify the region that is shaded in both the graphs. This region represents the solution to the system of linear inequalities.
In this case, the shaded region where both inequalities overlap is the area above the first dashed line and below the second dashed line.
Note: The solution to this system of inequalities is not a specific point but a region of the graph since there are infinitely many values of x and y that satisfy the given conditions.
This graphical representation helps visualize the solution to the system of linear inequalities.