Which region represents the solution to the system shown here? y –3x + 5 and y 0.5x – 1 i ii iii iv?

Answer: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 – 1We 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 = 60x = [tex]\frac{12}{7}=1.71[/tex](approx)Put x = [tex]\frac{12}{7}[/tex]  in (3) , we get,10y = 5 - 10  [tex]10y = 5(\frac{12}{7})- 10\\\\\Rightarrow y=-0.143[/tex]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.