Question

A system of linear inequalities is shown below.

x - y > 3
y + x ≤ 2

Describe the steps to graph the solution set to the system of inequalities.

Answer 1

you have to get y by itself on one side of the inequality sign. subtract x from both sides for each inequality since there is a positive sign in front of each. you do the opposite.
1. x(-x) -y> 3(-x) = -y > 3 - x
2. y + x(-x) <2(-x)= y < 2 - x

Answer 2

Can you help me do that @queenofdrillz

Answer 3

1. x(-x) -y> 3(-x) = -y > 3 - x
2. y + -x^2 <-2x= y < 2 - x

I can get that far...

Answer 4

what do you need help with? graphing it?

Answer 5

Yeah and describing the steps to get to graphing it

Answer 6

well y=mx+b would be the slope intercept form to use to graph it. i havent graphed much lately so i cant remember exactly how to. but try plugging your equations into that one. (because you have nothing in front of your x to equal m, m is automatically 1. because you dont have a plus sign for "+b", just use the minus sign. only difference is that its negative).

Answer 7

@Hero

Answer 8

x - y > 3
-y > -x + 3 -->(-1)
y < x - 3

y intercept is (0,-3)
slope is 1
x intercept is :
0 = x - 3
x = 3 ...x intercept is (3,0)

plot your intercepts (0,-3) and (3,0)....now start at y intercept (0,-3) and since slope is 1, go up 1 and to the right 1, and keep doing this and you should cross the x axis at (3,0). And since there is no equal sign, the line is dashed and since the inequality sign is less then, shading goes below the line.

Next line..
y + x <= 2
y <= -x + 2

slope is -1
y intercept is (0,2)
x intercept is (2,0)

plot your intercepts (0,2) and (2,0)...start at the y intercept (0,2) and since the slope is -1, come down 1 and to the right 1, then down 1, then to the right 1, and you should cross the x axis at (2,0). And since there is an equal sign, the line is solid. And since the sign is less then, shading is below the line.

Does that help ?