Question

How do you find the solution area to a system of inequalities? 100 points

Answer 1

Answer:

to find the area, first rearrange your equations into the format of y = mx + b

and y = ax + c

then plot these on a graph

for the first equation, shade above if y > mx + b and shade below if y < mx + b, and repeat for the second equation

the solution area would be the parts where both shaded areas intersect

Step-by-step explanation:

Answer 2

How To Solve Systems of Inequalities Graphically

1) Write the inequality in slope-intercept form or in the form  

y

=

m

x

+

b

y=mx+b

.

For example, if asked to solve  

x

+

y

≤

10

x+y≤10

, we first re-write as  

y

≤

−

x

+

10

y≤−x+10

.

2) Temporarily exchange the given inequality symbol (in this case  

≤

≤

) for just equal symbol. In doing so, you can treat the inequality like an equation. BUT DO NOT forget to replace the equal symbol with the original inequality symbol at the END of the problem!

So,  

y

≤

−

x

+

10

y≤−x+10

becomes  

y

=

−

x

+

10

y=−x+10

for the moment.

3) Graph the line found in step 2. This will form the "boundary" of the inequality -- on one side of the line the condition will be true, on the other side it will not. Review how to graph a line here.

4) Revisit the inequality we found before as  

y

≤

−

x

+

10

y≤−x+10

. Notice that it is true when y is less than or equal to. In step 3 we plotted the line (the equal-to case), so now we need to account for the less-than case. Since y is less than a particular value on the low-side of the axis, we will shade the region below the line to indicate that the inequality is true for all points below the line:

 

5) Verify. Plug in a point not on the line, like (0,0). Verify that the inequality holds. In this case, that means  

0

≤

−

0

+

10

0≤−0+10

, which is clearly true. We have shaded the correct side of the line.