how to show these:

Question

graph:

0<x<1 , 0<y<x

0<y<1 , 0<x<y

Answer 1

Hello, so the objective is to sketch a couple lines on your graph and then shade in the certain area that is described by the inequalities.

For the first one:

0<x<1 , 0<y<x

The first part, 0<x<1, is telling us that x can only be between 0 and 1.

Sketch vertical lines at x=0 and x=1.

The second part, 0<y<x, is telling us that y can only be between 0 and x.

Sketch the line of the simple graph y=x, and the horizontal line y=0.

Now, shade in the area where x is between 0 and 1 AND y is between 0 and x.

The answer is a triangle shape! (shaded below the line y=x)

For the second one:

0<y<1 , 0<x<y

The first part, 0<y<1, is telling us that y can only be between 0 and 1.

Sketch horizontal lines y=0 and y=1.

The second part, 0<x<y, is telling us that x can only be between 0 and y.

Sketch the line of the graph y=x, and the vertical line x=0.

Now, shade in the area where y is between 0 and 1 AND x is between 0 and y.

The answer is a triangle shape!

Note it is a different triangle than the first problem! This one is shaded above the line y=x!