Question

Which graph represents the system of inequalities? y+2<5xy+3x>4y≥2x

Answer 1

The graph that represents the system of inequalities is graph 3

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

The given system of inequalities

$y+2$

$y+3x>4$

$y\geq 2x$

Inequality (1) can be written as

$y$

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.