Question

Which system of linear inequalities is represented by the graph?

Answer 1

The answer to this is B

Answer 2

The correct option is 2.

Explanation:

From the given graph it is clear that the y-intercept of red line is 1 and y-intercept of blue line is 4.

The red line passes through the points (0,1) and (5,0). So, the slope of red line is

`m_R=(0-1)/(5-0)=-(1)/(5)`

The blue line passes through the points (-2,0) and (0,4). So, the slope of blue line is

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

The slope intercept form of a line is

`y=mx+b`

Where m is slope and b is y-intercept.

The y-intercept of red line is 1 and slope is
`-(1)/(5)`.

`y=-(1)/(5)x+1`

Multiply both sides by 5.

`5y=-x+5`

Add x on both the sides.

`x+5y=5`

The related equation of red line is x+5y=5.

The shaded region is above the line and the related line is a solid line, therefore the sign of inequality is ≥. So, the first inequality is

`x+5y\geq 5`

The y-intercept of blue line is 4 and slope is 2.

`y=2x+4`

The related equation of blue line is y=2x+4.

The shaded region is below the line and related line is a solid line, therefore the sign of inequality is ≤. So, the second inequality is

`y\leq 2x+4`

Therefore the correct option is 2.