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 – 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 = [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.
