Solve each system of inequalities by graphing.

Question

 1.  x > 5 

    y ≤ 4    

 

 

2.

 y > 3

y > -x + 4

Answer 1

1) Given system x > 5

y ≤ 4

Draw the coordinate plane.

Graph the lines y = 4 and x = 5.

The boundary of the graph y ≤ 4 solid and shaded in blue colour.

To know the which part is shading substitute the (0,0) in y ≤ 4.

0 ≤ 4

The statement is true.

So the origin containing part is shading now and it is in teal colour.

And  the boundary of the graph of x > 5 is dotted in red colour.

The graph of x > 5 is shaded in fuchsia colour.

The solution of system is the set of orderd pairs in the intersection of the graph of x > 5 and y ≤ 4

This region is shaded in light purple colour.

Answer 2

2) Given system y > 3

y > -x+4

Graph the lines y = 3 and y = -x+4.

To know the which region is shading, substitute the (0,0) in given inequalities.

Then 0  > 3 and 0 > 4.

The above statements are false.

Now shade the regions with out origin contaning parts.

The boundary line of the graph of y >3 is dotted in blue colour.

The boundary line of the graph of y > -x+4 is dotted in red colour.

The solution of the system is the set of orderd pairs in the intersection of the graph y >3 and y > -x+4.

This regeion is shaded light purple colour.