ABCD is a parallelogram. Find the value of x, y and z.​

The region represents the solution to the given system is region iv.

Step-by-step explanation:

Given : system of linear equation  y = –3x + 5 and y =  0.5x – 1

We have to find the  region that represents the solution to the system.

Consider the given system  

y = –3x + 5 .....(1)

y =  0.5x – 1    ..........(2)

Multiply (2) by 10, we have,

10y = 5x - 10  ....(3)

Multiply equation (1) by 10, we have,

10y = –30x + 50 ..........(4)

Subtract (3) and (4) , we have,

10y - 10y = –30x + 50 - ( 5x - 10 )

Simplify, we have,

0 = –30x + 50 - 5x + 10  

35x = 60

x = (approx)

Put x =  in (3) , we get,

10y = 5 - 10  

Thus, point of solution is (1.71, -0.143)

Since,  (1.71, -0.143) lies in Fourth quadrant.

So the region represents the solution to the given system is region iv.