Question

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

Answer 1

D / IV

Explanation:

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Answer 2

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

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 =
`(12)/(7)=1.71`(approx)

Put x =
`(12)/(7)` in (3) , we get,

10y = 5 - 10

`10y = 5((12)/(7))- 10\\\\\Rightarrow y=-0.143`

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.