Write a system of linear equations represent by the graph

inequality 1:

inequality 2:

From graph,

inequality 1:  y > x+(-2)

inequality 2: y > (-4)x+2

Step-by-step explanation:

The graph shows two lines on the X-Y plane.

Step 1: Find the equation of a line.

From figure, One line is passing through (3,0) and (0,-2)

Slope of line is given by m=

m=

m=

Y-intercept isc=(-2)

The equation of line is given by y=mx+c

Therefore, y=x+(-2)

From figure, Another line is passing through (0.5,0) and (0,2)

Slope of line is given by m=

m=

m=

m=(-4)

Y-intercept isc=(2)

The equation of line is given by y=mx+c

Therefore, y=(-4)x+2

Step 2: Test of origin and finding inequality

For y=x+(-2)

Let suppose,  y > x+(-2)

This line is shaded toward the origin then, inequality must satisfy the origin

Test for origin says,

0 > (0)+(-2)

0 > (-2)

TRUE.

y > x+(-2) is required inequality

For y=(-4)x+2

Let suppose, y > (-4)x+2

This line is shaded away from the origin then, inequality must not satisfy the origin

Test for origin says,

0 > (0)+(-2)

0 > (+2)

FALSE, so that y > (-4)x+2 does not satisfy the origin

y > (-4)x+2 is required inequality

Thus,

inequality 1:  y > x+(-2)

inequality 2: y > (-4)x+2