Question

Which graph represents the system of inequalities?

y+2<5xy+3x>4y≥2x

Answer 1

The correct option is 2.

Explanation:

The given system of inequalities

`y+2<5x`

`y+3x>4`

`y\geq 2x`

Inequality (1) can be written as

`y<5x-2`

The related equation is

`y=5x-2`

The slope of line is 5 and y-intercept is -2.

The sign of inequality is < , it means related line of inequality (1) is a dotted line and shaded region is below the line.

Inequality (2) can be written as

`y>-3x+4`

The related equation is

`y=-3x+4`

The slope of line is -3 and y-intercept is 4.

The sign of inequality is >, it means related line is a dotted line and shaded region is above the line.

Inequality (3) is

`y\geq 2x`

The related equation is

`y=2x`

The slope of line is 2 and y-intercept is 0.

The sign of inequality is ≥, it means related line is a solid line and shaded region is above the line.

In the below graph the common shaded region is the solution region.

Therefore the correct option is 2.