Which system of linear inequalities is represented

Ответ:

goargrant

03.01.2022

The correct option is 2.

Step-by-step 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

$m_R=\frac{0-1}{5-0}=-\frac{1}{5}$

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

$m_B=\frac{4-0}{0-(-2)}=2$

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 $-\frac{1}{5}$ .

$y=-\frac{1}{5}x+1$

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.

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