Question

Which system of linear inequalities is represented by the graph?

x – 3y > 6 and y > 2x + 4
x + 3y > 6 and y > 2x – 4
x – 3y > 6 and y > 2x – 4
x + 3y > 6 and y > 2x + 4

Answer 1

The answer is D

x + 3y > 6 and y > 2x + 4

Answer 2

Option (d) is correct.

`3y+x>6` and
`y>2x+4`

Explanation:

Given : A graph

We have to choose the system of linear inequalities is represented by the graph .

Let take two points on each line

We have (0,2) and (6,0) on one line

Then equation of line is of the form y = mx + b , where, m is slope and b is y- intercept.

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(6,\:0\right)`

`m=(0-2)/(6-0)=(-1)/(3)`

Thus, Equation of line is
`y=(-1)/(3)x+2`

Simplify, we have,

`3y+x=6`

Since, (3,2) is the point in the region so substitute, we get,

`3(2)+3>6`

Therefore, Inequality becomes,
`3y+x>6`

Similarly, for second line

We have (0,4) and (-2,0) on one line

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`m=(0-4)/(-2-0)=2`

Thus, Equation of line is
`y=2x+4`

Since, (-3,1) is the point in the region so substitute, we get,

`1>-6+4=-2`

Therefore, Inequality becomes,
`y>2x+4`

Thus, Inequality becomes

`3y+x>6` and
`y>2x+4`