linear inequalities

Question

What are the equations of the boundary lines in the form y=... for these two inequalities

 I) 2y+3x> 11

II) 2y> 10x-7

        The second equation should a greater of equal to sign.

 

2) Determine the coordinates of the point of intersection 

 

 

Answer 1

Amy,

 

The equation for first part is

 

2y + 3x > 11

subtract 3x from both sides

2y > 11-3x

Divide by 2 on both sides

y > 5.5 -1.5x

 

For second part the equation is 

2y >= 10x -7

y >= 5x -3.5

 

To find the co-ordinates at point of intersection you have to use equality between Right side and left side of equations

so y = 5.5-1.5x also y = 5x -3.5

so 5.5 -1.5x = 5x -3.5

6.5 x = 9

x = 1.38

y = 5x -3.5= 5*1.38 - 3.5 = 3.4