Algebra homework

Question

1. Create a example of a linear inequality in two variables.
2. Find one solution that satisfies your linear inequality and find one solution that does not satisfy your linear inequality.
3. Describe the steps and show how you would find all the solutions of the linear inequality.
4. What is you had used a different inequality symbol, how would that have changed your solution?

Answer 1

y > -x + 5

y <= x +1

Inequality #1: intercept at (0,5); slope is -1; dashed/dotted line

the origin (0,0) is NOT a solution because 0 > 5 is false, so

shades AWAY from the origin with RED

Inequality #2: intercept at (0,1); slope is 1; solid line

the origin (0,0) IS a solution because 0 <= 1 is TRUE, so

shades TOWARDS the origin with BLUE

they meet at -x + 5 = x+1

5 = 2x + 1

4 = 2x

x = 2

(2,3)

the solution set begins at (2,3) and proceeds in the northeast direction with slope m=1 with solid line;

it also proceeds southeast from (2,3) with slope -1 with dotted/dashed line.

It is shaded with purple, above the dotted line but below the solid one

One possible solution is (6,4), which satisfies BOTH inequalities

(2,6) satisfies the first inequality but not the second

reversing the inequalities changes the direction of the shading

(-2,0) satisfies NEITHER inequality is NOT a solution of either inequality.

It is in the unshaded (white) section

(2,0) satisfies the second inequality but not the first